SPH102 Third CAT March 2023 SOLVED

(1)  A ray of light is incident in air on the surface of a glass block of refractive index 1.5. If the angle of incidence is 30⁰, calculate:

(a) the angle of refraction

(b) the amount by which the ray is deviated on entering the glass

(2) A block of glass measures 5 cm x 5 cm x 8 cm. When the block is stood on its smaller faces and viewed directly from above, it appears to be a cube. Calculate the refractive index of glass. 

(3) A ray of monochromatic light is incident on one face of a glass prism of refractive index 1.5. Calculate the least angle of incidence for the ray to be transmitted through the second face.

Consider a ray incident on face AB.

)                            (i)

For the ray to emerge from face AC, the angle r’ should be less than the critical angle that is,;                          

From tringle AMN

Equation (i) therefore becomes

(4) Calculate the critical angle for a glass-air surface if a ray of light which is incident in air on the surface is deviated through 15.5⁰ when its angle of incidence is 40⁰.

(5)  1.4 m tall child with eyes 10 cm below the top of her head wishes to see her whole standing self on a vertical plane mirror.

(a) Find the minimum length of the mirror that makes this possible. 

(b) How far above the ground is the top of the mirror

(6) An object is placed 4 cm from;

(a) Concave mirror which has a radius of curvature of 24 cm

(b) Convex mirror of radius of curvature of 40 cm

Calculate the magnification of the image produced in each case.

Concave, f is positive;

Convex, f is negative; 

(7) A rod which is 10 cm long is placed along the principal axis of a concave mirror such that the mid-point of the rod is 35 cm from the pole of the mirror. Calculate the radius of curvature of the mirror if it forms a real image of the rod which is 20 cm long. 

Dr. Margaret W. Chege