# Physics Class 12 NCERT Solutions: Chapter 9 Ray Optics and Optical Instruments Part 3

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Q: 6. A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is measured to be. What is the refractive index of the material of the prism? The refracting angle of the prism is . If the prism is placed in water (refractive index 1.33), predict the new angle of minimum deviation of a parallel beam of light.

Angle of minimum deviation,

Angle of the prism,

Refractive index of water,

Refractive index of the material of the prism

The angle of deviation is related to refractive index as:

Hence, the refractive index of the material of the prism is.

Since the prism is placed in water, let be the new angle of minimum deviation for the same prism.

The refractive index of glass with respect to water is given by the relation:

Hence, the new minimum angle of deviation is.

Q: 7. Double- convex lenses are to be manufactured from a glass of refractive index, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be?

Refractive index of glass,

Focal length of the double-convex lens,

Radius of curvature of one face of the lens

Radius of curvature of the other face of the lens

Radius of curvature of the double-convex lens

The value of can be calculated as:

Hence, the radius of curvature of the double-convex lens is.

Q: 8. A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam from P. At what point does the beam converge if the lens is (a) a convex lens of focal length, and (b) a concave lens of focal length?

In the given situation, the object is virtual and the image formed is real.

Object distance,

(a) Focal length of the convex lens,

Image distance

According to the lens formula, we have the relation:

Hence, the image is formed away from the lens, toward its right.

(B) Focal length of the concave lens,

Image distance

According to the lens formula, we have the relation:

Hence, the image is formed away from the lens, toward its right.