Physics Class 12 NCERT Solutions: Chapter 9 Ray Optics and Optical Instruments Part 9

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Formula of focal length

Formula of Focal Length

Q: 18. Answer the following questions:

(A) You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.

(B) A virtual image, we always say, cannot be caught on a screen.

Yet when we ‘see’ a virtual image, we are obviously bringing it on to the ‘screen’ (i.e., the retina) of our eye. Is there a contradiction?

(C) A diver under water, looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?

(D) Does the apparent depth of a tank of water change if viewed obliquely? If so, does the apparent depth increase or decrease?

(E) The refractive index of diamond is much greater than that of ordinary glass. Is this fact of some use to a diamond cutter?

Answer:

(A) Yes

Plane and convex mirrors can produce real images as well. If the object is virtual, i.e., if the light rays converging at a point behind a plane mirror (or a convex mirror) are reflected to a point on a screen placed in front of the mirror, then a real image will be formed.

(B) No

A virtual image is formed when light rays diverge. The convex lens of the eye causes these divergent rays to converge at the retina. In this case, the virtual image serves as an object for the lens to produce a real image.

(C) The diver is in the water and the fisherman is on land (i.e., in air). Water is a denser medium than air. It is given that the diver is viewing the fisherman. This indicates that the light rays are travelling from a denser medium to a rarer medium. Hence, the refracted rays will move away from the normal. As a result, the fisherman will appear to be taller.

(D) Yes; Decrease

The apparent depth of a tank of water changes when viewed obliquely. This is because light bends on travelling from one medium to another. The apparent depth of the tank when viewed obliquely is less than the near-normal viewing.

(E) Yes

The refractive index of diamond is more than that of ordinary glass. The critical angle for diamond is less than that for glass. A diamond cutter uses a large angle of incidence to ensure that the light entering the diamond is totally reflected from its faces. This is the reason for the sparkling effect of a diamond.

Q: 19. The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?

Answer:

Distance between the object and the image,

Maximum focal length of the convex lens

For real images, the maximum focal length is given as:

Hence, for the required purpose, the maximum possible focal length of the convex lens is.

Q: 20. A screen is placed from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by. Determine the focal length of the lens.

Answer:

Distance between the image (screen) and the object,

Distance between two locations of the convex lens,

Focal length of the lens

Focal length is related to and as:

Therefore, the focal length of the convex lens is .

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