Answers to Problems on (Optical Instruments) HC Verma's Questions for Short Answer

 Q#1

Can a virtual image be formed on the retina in a seeing process?

Answer:
No. The retina is like a screen on which only real images can be formed.

Q#2
Can the image formed by a simple microscope be projected on a screen without using any additional lens or mirror?

Answer:
The image formed by a simple microscope is a virtual image hence it cannot be projected on a screen without using some additional lens or mirror.

Q#3
The angular magnification of a system is less than one. Does it mean that the image formed is inverted?

Answer:
The angular magnification of a system is the ratio of the angle subtended by the final image to the angle subtended by the object on the eye. Its value less than one means the reduced size of the final image not that it is inverted.

Q#4
A simple microscope using a single lens often shows a colored image of a white source. Why?

Answer: 
A white source of the light consists of different colors of light having different wavelengths. These colors of light bend differently after refraction through a simple microscope which consists of a single convex lens. It means the focal length of the lens is different for a different color of light. Hence, a simple microscope often shows a colored image of a white source.

Q#5
A magnifying glass is a converging lens placed closed to the eye. A farsighted person uses spectacles having converging lenses. Compare the functions of a converging lens used as a magnifying glass and as spectacles.

Answer:
The converging lens used as a magnifying glass increases the angle subtended by the object on the eye. It functions as an angular magnifier. Its focus is small and an object placed within the focal length makes an image at the least distance of the distinct vision (with adjustment).

A farsighted person cannot see an object placed at the normal least distance of clear vision because the image of the object cannot form on the retina due to the inability of the eye lens or due to decrease in the distance between eye-lens and the retina. In such a case the converging lens in the spectacles helps to form the image at the retina.

Q#6
A person is viewing an extended object. If a converging lens is placed in front of his eyes, will he feel that the size has increased?

Answer:
It depends upon the distance of the object from the eye and the focal length of the converging lens. If the object is at a large distance (infinity) then the person will not see it clearly with a converging lens in front of his normal eyes.
If the object is nearer, the person will feel that the size has increased.

Q#7
The magnifying power of a converging lens used as a simple microscope is (1+D/f). A compound microscope is a combination of two such converging lenses. Why don't we have magnifying power (1+D/fₒ)(1+D/fₑ)? In other words, why can the objective not be treated as a simple microscope but the eyepiece can?

Answer:
The objective cannot be treated as a simple microscope because in a simple microscope the object is placed within the focal length so that the image is formed at the least distance of clear vision for angular magnification. In the case of objective, the object is slightly away from the focal point and the image is real and inverted and just inside the focal length of the eyepiece.
But the eyepiece fulfills these criteria of the simple microscope.

Q#8
By mistake, an eye surgeon puts a concave lens in place of the lens in the eye after a cataract operation. Will the patient be able to see clearly any object placed at any distance?

Answer:
After the cataract operation the eye needs a converging lens to form a real image on the retina. If a concave lens is put in the eye, the rays inside the eye will diverge and a virtual image will be formed outside of the eye. So the patient will not be able to see clearly any object at any distance.

Q#9
The magnifying power of a simple microscope is given by 1+D/f, where D is the least distance for the clear vision. For farsighted persons, D is greater than the usual. Does it mean that the magnifying power of a simple microscope is greater for a farsighted person as compared to a normal person? Does it mean that a farsighted person can see an insect more clearly under a microscope than a normal person?

Answer: 
The magnifying power of a simple microscope is given by
m = 1+D/f.
For a far-sighted person, D > Dₙ (Dₙ- for a normal person), hence the magnifying power of a simple microscope is greater for a farsighted person. And hence a farsighted person can see an insect more clearly under a microscope than a normal person.

Q#10
Why are the magnification properties of microscopes and telescopes are defined in terms of the ratio of the angles and not in terms of the ratio of sizes of objects and images?

Answer: 
The size of an object as sensed by us is related to the size of the image formed on the retina. A larger image on the retina activates a larger number of rods and cones (on the retina) attached to it and the object looks larger. An object of the same size at a greater distance makes a smaller image on the retina and it looks smaller because it subtends a lesser angle at the eye than an object nearer to the eye. This angle is called a visual angle. So the size of the image cannot be used for magnification properties of microscopes and telescopes because different sizes of images may subtend same visual angle on the eye and the same size of the image on the retina may be formed and the difference cannot be sensed by the eye.
Hence the magnification properties of microscopes and telescopes are defined in terms of the ratio of the angles and not in terms of the ratio of sizes of objects and images.

Q#11
An object is placed at a distance of 30 cm from a converging lens of focal length 15 cm. A normal eye (near point 25 cm, far point infinity) is placed closed to the lens on the other side. (a) Can the eye see the object clearly? (b) What should be the minimum separation between the lens and the eye so that the eye can clearly see the object? (c) Can a diverging lens, placed in contact with the converging lens, help in seeing the object clearly when the eye is close to the lens?

Answer:
(a) Let us find out the place of the image formed by the lens. Here u= -30 cm, f = 15 cm, v =? From the lens formula,

1/v - 1/u = 1/f
1/v + 1/30 = 1/15
1/v = 1/15 - 1/30 = 1/30
v = 30 cm  

Thus the image is formed 30 cm behind the lens and hence behind the eye. The eye cannot see the object clearly.

(b) Since the least distance of clear vision is 25 cm. The minimum distance of the eye from the lens should be

25 + 30 = 50 cm.

(c) A diverging lens placed in contact with the converging lens will make the focal length of the converging lens larger. If the combined focal length of the lens be F and a virtual image is formed at D = 25 cm, then the eye will see the object clearly.

1/F = 1/(-25) - 1/(-30) = 1/30 - 1/25 = (5 - 6)/150
1/F = -1/150
F = -150 cm
Let the focal length of the diverging lens = f

Hence 1/F = 1/15 + 1/f
1/f = -1/150 - 1/15 = -11/150
f = -150/11 = -13.64 cm

Thus if the focal length of the diverging lens is 13.64 cm, then the eye can see clearly.

Q#12
A compound microscope forms an inverted image of an object. In which of the following cases it is likely to create difficulties? (a) Looking at small germs. (b) Looking at circular sports. (c) looking at a vertical tube containing some water.

Answer:
In the case (c). Since a germ or a circular spot has no specified upper or lower point, there is no problem in seeing it erect or inverted. But a vertical tube containing some water when viewed through this microscope will look having water defying the gravity and the meniscus profile just the opposite.   

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