Microscopes

Microscope and Telescopes Q.1 A converging lens of focal length 6.25 cm is used as a magnifying glass. If the near point of the observer is 25 cm form the eye and the lens is held close to the eye, calculate (a) the distance of the object from the lens and (b) the angular magnification. Find the angular magnification when the final image is formed at infinity. [Ans. (a) – 5 cm, (b) 4] Q.2 The focal lengths of the objective and the eyepiece of a compound microscope are 1.0 cm and 5.0 cm respectively. An object, placed at a distance of 1.1 cm from the objective has its final image formed at (i) infinity, (ii) least distance of distinct vision. Find the magnifying power and the distance between the lenses. Least distance of distinct vision is 25 cm. [Ans. (i) -50, (ii) -60] Q.3 The distance between the objective and the eye-piece in a microscope set in a horizontal direction is 12 cm and their respective focal lengths are 0.6 cm and 5 cm. If a clear image is to be obtained at 25 cm to the left of the eye-piece, find (i) the initial position of the object, and (ii) the magnification. [Ans. - 0.65 cm, -72.3] Q.4 The focal lengths of the eyepiece and the objective of a compound microscope are 5 cm and 1 cm respectively and the length of the tube is 20 cm. Calculate the magnifying power of the microscope when the final image is formed at infinity. The least distance of distinct vision is 25 cm. [Ans. -70] Q.5 The focal lengths of the objective and the eyepiece of an astronomical telescope are 140 cm and 5.0 cm respectively. Find the magnifying power of the telescope for viewing distant objects when (a) the final image is formed at the least distance of distinct vision (25 cm), (b) the telescope is in normal adjustment (that is, the final image is formed at infinity). (c) What is the separation between the objective and eyepiece in case (b)? [Ans. -33.6, -28, 145 cm] Q.6 A telescope has an objective of focal length 30 cm and an eyepiece of focal length 3.0 cm. It is focused on a scale distant 2.0 meter. For seeing with relaxed eye, calculate the separation between the objective and the eyepiece. [Ans. 38.3 cm] Q.7 What is visual angle? Does it vary with distance of the object from the eye? Ans. It is the angle subtended by an object at the eye. It decreases with increasing distance of the object from the eye. Q.8 Distant objects which appear quite small with nacked eye, a appear larger through a telescope; how? Ans. The telescope forms the image of the distant object near the eye. Therefore, the image subtends a large visual angle at the eye. Q.9 What is the angular magnification produced by a single convex lens used as a simple microscope in ‘normal’ use ? Ans. M = D / (, where D is least distance of distinct vision and ( is focal length of the lens. Q.10 An object is seen first in red light and then in violet light through a simple microscope. In which case will the magnifying power larger? Ans. Magnifying power of a simple microscope in normal use is D/(. As (V < (R, the magnifying power will be larger for violet light. Q.11 What is difference between linear magnification and angular magnification (also called magnifying power) produced by a lens? Ans. The linear magnification produced by a lens is the ratio of the size of the image to the size of the object and is equal to the ratio of the image and object distances, that is, m = (/u. On the other hand, angular magnification is the ratio of the angle subtended at the eye by the image to the angle subtended by the object seen directly when both are located at the least distance of distinct vision (D). It is given by M = D/ u = 1 + D / ( In the special case when ( = D, m becomes equal to M. Q.12 Why is, in a microscope, objective lens of a small aperture is taken? Ans. Microscope is used to observe very small objects placed very close to it. Therefore, if the aperture of the objective is large then light coming from the object will spread in large aperture and the object will be seen less bright. On the other hand, if aperture is small, then light will spread in small aperture and the image formed will be more bright. Q.13 What steps are taken to obtain a high angular magnification from a compound microscope? Ans. Both the objective and the eyepiece are taken of small focal lengths, the focal length of the eyepiece being slightly longer. Q.14 Express the magnifying power (angular magnification) of an astronomical telescope in terms of the focal length of the objective and the eyepiece. Ans. M = - (0 / (e (1 + (e / D) when the final image is formed at the least distance of distinct vision, and M = - (0 / (e , when the final image is formed at infinity. M = - (0 and (e are focal lengths of objective and eyepiece respectively. Q.15 In a telescope, the objective has a large aperture while the eyepiece has a small aperture. Why? Ans. Objective of ‘large’ aperture is taken so that it may collect sufficient light and form bright images of very distant objects (stars, etc.). Moreover, large-aperture objective provides greater resolving power to the telescope. On the other hand eyepiece of ‘small’ aperture is taken so that whole of the light forming the image may enter the small pupil of the eye. Q.16 The magnifying powers of two telescopes are same but the aperture of their objectives are different. What will be the different in the final images formed by them? Ans. There will be difference in the brightness of the images and in the resolving limit. Q.17 Why is parabolic mirror often used in terrestrial reflecting telescope? Q.18 How will you distinguish between a compound microscope and a telescope simply by seeing them? Ans. The aperture of the objective of a compound microscope is much smaller, whereas the aperture of the objective of a telescope is much larger than that of the eyepiece. Q.19 In a telescope the objective is larger and the eyepiece is smaller. In a microscope the objective is smaller and the eyepiece is larger. If a telescope is inverted, will it be able to work as microscope? Is the reverse of this possible? Ans. No, because the difference in the focal lengths of the two lenses in a microscope is very small. Hence, on inverting the telescope, its magnifying power in the form of microscope will be very small. Similarly, on inverting a microscope, its magnifying power in the form of telescope will be very small. Q.20 The magnifying power of a simple microscope is inversely proportional to the focal length of the lens. Then, why can we not obtain a very high magnifying power by using a lens of very small focal length? Ans. For a very high magnifying power, the focal length of the lens would have to the very small. Lenses of very small focal length are not easy to manufacture. Secondly, such lenses would be very thick in the middle and cause appreciable dispersion of light due to their prismatic action. Hence they will produce coloured image (chromatic aberration). Q.21 Two lenses of focal lengths 5 cm and 50 cm are to be used for making a telescope. Which lens will you use for the objective? Ans. The magnifying power of a telescope, for relaxed eye, is M = (0 / (e. Hence, for a higher magnifying power, the lens of larger focal length (50 cm) is to be used objective. Q.22 Which two of the following lenses L1 , L2 and L3 will you select for constructing a best possible (i) telescope, (ii) microscope. Which of the selected lenses is to be used as objective and which as eyepiece in each case? Lenses Power (P) Aperture (A) L1 6 D 1 cm L2 3 D 8 cm L3 10 D 1 cm Ans. (i) A telescope requires an objective of large focal length and large aperture, and an eyepiece of much smaller focal length and aperture. Hence L2 is to be used as objective (focal length and aperture largest) and L3 as eyepiece (focal length and aperture smallest). A microscope requires an objective of very small focal length and small aperture, and an eyepiece of slightly longer focal length and larger aperture. Hence L3 is to be used as objective and L1 as eyepiece. Q.23 In what ratio will the intensity of the image increase when the aperture (diameter) of the objective of an astronomical telescope is doubled? Is there any effect on the magnifying power of the telescope? Ans. On doubling the aperture, the area of the objective lens will become four times and so the light gathering capacity of the telescope will also be four times. Hence the intensity of the image will increase to four times. There is, however, no effect on the magnifying power of the telescope. Q.24 An object is seen through a simple microscope of focal length 12 cm. Find the angular magnification produced if the image is formed at the near point of the eye which is 25 cm away from it.[Ans= 3.08] Q.25 A 10 D lens is used as a magnifier. Where should the object be placed to obtain maximum angular magnification for a normal eye (near point = 25 cm)? [Ans=-7.1] Q.26 A small object is placed at a distance of 3.6 cm from a magnifier of focal length 4.0 cm. Find the position of the image. Find the linear magnification. Find the angular magnification. Q.27 A compound microscope consists of an objective of focal length 1.0 cm and an eyepiece of focal length 5.0 cm separated by 12.2 cm. At what distance from the objective should an object be placed to focus it properly so that the final image is formed at the least distance of clear vision (25 cm)? Calculate the angular magnification in this case. [Ans=(a) –1.1 cm (b) - 44] Q.28 The separation L between the objective (f = 0.5 cm) and the eyepiece (f = 5 cm) of a compound microscope is 7 cm. Where should a small object be place so that the eye is least strained to see the image? Find the angular magnification produced by the microscope. [Ans= -15] Q.29 An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 4.0 cm. The telescope is focused to see an object 10 km from the objective. The final image is formed at infinity. Find the length of the tube and the angular magnification produced by the telescope. [Ans=-50] Q.30 A Galilean telescope is constructed by an objective of focal length 50 cm and an eyepiece of focal length 5.0 cm. Find the tube length and magnifying power when it is used to see an object at a large distance in normal adjustment, If the telescope is to focus an object 2.0 m away from the objective, what should be the tube length and angular magnification, the image again forming at infinity? [Ans=(a) 10, (b) 13.33] Q.31 A compound microscope has a magnifying power of 100 when the image is formed at infinity. The objective has a focal length of 0.5 cm and the tube length is 6.5 cm. Find the focal length of the eyepiece. [Ans=2 cm] Q.32 A compound microscope consists of an objective of focal length 1 cm and an eyepiece of focal length 5 cm. An object is placed at a distance of 0.5 cm from the objective. What should be the separation between the lenses so that the microscope projects an inverted real image of the object on a screen 30 cm behind the eyepiece? [Ans= 5 cm] Q.33 An optical instrument used for angular magnification has a 25 D objective and a 20 D eyepiece. The tube length is 25 cm when the eye is least strained. Whether it is a microscope or a telescope? What is the angular magnification produced? [Ans=(a) Microscope, 20] Microscope and Telescopes Q.1 A converging lens of focal length 6.25 cm is used as a magnifying glass. If the near point of the observer is 25 cm form the eye and the lens is held close to the eye, calculate (a) the distance of the object from the lens and (b) the angular magnification. Find the angular magnification when the final image is formed at infinity. [Ans. (a) – 5 cm, (b) 4] Q.2 The focal lengths of the objective and the eyepiece of a compound microscope are 1.0 cm and 5.0 cm respectively. An object, placed at a distance of 1.1 cm from the objective has its final image formed at (i) infinity, (ii) least distance of distinct vision. Find the magnifying power and the distance between the lenses. Least distance of distinct vision is 25 cm. [Ans. (i) -50, (ii) -60] Q.3 The distance between the objective and the eye-piece in a microscope set in a horizontal direction is 12 cm and their respective focal lengths are 0.6 cm and 5 cm. If a clear image is to be obtained at 25 cm to the left of the eye-piece, find (i) the initial position of the object, and (ii) the magnification. [Ans. - 0.65 cm, -72.3] Q.4 The focal lengths of the eyepiece and the objective of a compound microscope are 5 cm and 1 cm respectively and the length of the tube is 20 cm. Calculate the magnifying power of the microscope when the final image is formed at infinity. The least distance of distinct vision is 25 cm. [Ans. -70] Q.5 The focal lengths of the objective and the eyepiece of an astronomical telescope are 140 cm and 5.0 cm respectively. Find the magnifying power of the telescope for viewing distant objects when (a) the final image is formed at the least distance of distinct vision (25 cm), (b) the telescope is in normal adjustment (that is, the final image is formed at infinity). (c) What is the separation between the objective and eyepiece in case (b)? [Ans. -33.6, -28, 145 cm] Q.6 An object is seen through a simple microscope of focal length 12 cm. Find the angular magnification produced if the image is formed at the near point of the eye which is 25 cm away from it.[Ans= 3.08] Q.7 A 10 D lens is used as a magnifier. Where should the object be placed to obtain maximum angular magnification for a normal eye (near point = 25 cm)? [Ans=-7.1] Q.8 A small object is placed at a distance of 3.6 cm from a magnifier of focal length 4.0 cm. Find the position of the image. Find the linear magnification. Find the angular magnification. Q.9 A compound microscope consists of an objective of focal length 1.0 cm and an eyepiece of focal length 5.0 cm separated by 12.2 cm. (a) At what distance from the objective should an object be placed to focus it properly so that the final image is formed at the least distance of clear vision (25 cm)? (b) Calculate the angular magnification in this case. [Ans=(a) –1.1 cm (b) - 44] Q.10 The separation L between the objective (f = 0.5 cm) and the eyepiece (f = 5 cm) of a compound microscope is 7 cm. Where should a small object be place so that the eye is least strained to see the image? Find the angular magnification produced by the microscope. [Ans= -15] Q.11 An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 4.0 cm. The telescope is focused to see an object 10 km from the objective. The final image is formed at infinity. Find the length of the tube and the angular magnification produced by the telescope. [Ans=-50] Q.12 A compound microscope has a magnifying power of 100 when the image is formed at infinity. The objective has a focal length of 0.5 cm and the tube length is 6.5 cm. Find the focal length of the eyepiece. [Ans=2 cm] Q.13 A compound microscope consists of an objective of focal length 1 cm and an eyepiece of focal length 5 cm. An object is placed at a distance of 0.5 cm from the objective. What should be the separation between the lenses so that the microscope projects an inverted real image of the object on a screen 30 cm behind the eyepiece? [Ans= 5 cm] Q.14 An optical instrument used for angular magnification has a 25 D objective and a 20 D eyepiece. The tube length is 25 cm when the eye is least strained. Whether it is a microscope or a telescope? What is the angular magnification produced? [Ans=(a) Microscope, 20] Q.13 What steps are taken to obtain a high angular magnification from a compound microscope? Ans. Both the objective and the eyepiece are taken of small focal lengths, the focal length of the eyepiece being slightly longer. Q.15 In a telescope, the objective has a large aperture while the eyepiece has a small aperture. Why? Ans. Objective of ‘large’ aperture is taken so that it may collect sufficient light and form bright images of very distant objects (stars, etc.). Moreover, large-aperture objective provides greater resolving power to the telescope. On the other hand eyepiece of ‘small’ aperture is taken so that whole of the light forming the image may enter the small pupil of the eye. Q.16 The magnifying powers of two telescopes are same but the aperture of their objectives are different. What will be the different in the final images formed by them? Ans. There will be difference in the brightness of the images and in the resolving limit. Q.18 How will you distinguish between a compound microscope and a telescope simply by seeing them? Ans. The aperture of the objective of a compound microscope is much smaller, whereas the aperture of the objective of a telescope is much larger than that of the eyepiece. Q.19 In a telescope the objective is larger and the eyepiece is smaller. In a microscope the objective is smaller and the eyepiece is larger. If a telescope is inverted, will it be able to work as microscope? Is the reverse of this possible? Ans. No, because the difference in the focal lengths of the two lenses in a microscope is very small. Hence, on inverting the telescope, its magnifying power in the form of microscope will be very small. Similarly, on inverting a microscope, its magnifying power in the form of telescope will be very small. Q.20 The magnifying power of a simple microscope is inversely proportional to the focal length of the lens. Then, why can we not obtain a very high magnifying power by using a lens of very small focal length? Ans. For a very high magnifying power, the focal length of the lens would have to the very small. Lenses of very small focal length are not easy to manufacture. Secondly, such lenses would be very thick in the middle and cause appreciable dispersion of light due to their prismatic action. Hence they will produce coloured image (chromatic aberration). Q.21 Two lenses of focal lengths 5 cm and 50 cm are to be used for making a telescope. Which lens will you use for the objective? Ans. The magnifying power of a telescope, for relaxed eye, is M = (0 / (e. Hence, for a higher magnifying power, the lens of larger focal length (50 cm) is to be used objective. Q.22 Which two of the following lenses L1 , L2 and L3 will you select for constructing a best possible (i) telescope, (ii) microscope. Which of the selected lenses is to be used as objective and which as eyepiece in each case? Lenses Power (P) Aperture (A) L1 6 D 1 cm L2 3 D 8 cm L3 10 D 1 cm Ans. (i) A telescope requires an objective of large focal length and large aperture, and an eyepiece of much smaller focal length and aperture. Hence L2 is to be used as objective (focal length and aperture largest) and L3 as eyepiece (focal length and aperture smallest). A microscope requires an objective of very small focal length and small aperture, and an eyepiece of slightly longer focal length and larger aperture. Hence L3 is to be used as objective and L1 as eyepiece. Q.23 In what ratio will the intensity of the image increase when the aperture (diameter) of the objective of an astronomical telescope is doubled? Is there any effect on the magnifying power of the telescope? Ans. On doubling the aperture, the area of the objective lens will become four times and so the light gathering capacity of the telescope will also be four times. Hence the intensity of the image will increase to four times. There is, however, no effect on the magnifying power of the telescope. 6