A . Objective questions with only one correct answer –

1 . Rays of light from the sun falls on a biconvex lens of focal length *f *and the circular image of the Sun of radius r is formed on the focal plane of the lens . Then ,

- (a) area of image is π r² and area is directly proportional of
*f .* - (b) area of image is π r² and area is directly proportional to r².
- (c) intensity of image increases if
*f*is increased. - (d) if lower half of the lens is covered with black paper , area will become half .

2 . A ray of light travelling in water is incident on its surface open to air . The angle of incidence is θ , which is less than the critical angle . Then , there will be –

- (a) only a reflected ray and no refracted ray .
- (b) only a refracted ray and no reflected ray .
- (c) a reflected ray and a refracted ray and the angle between them would be less than 180° – 2 θ .
- (d) a reflected ray and a refracted ray and the angle between them would be greater than 180° – 2 θ .

3 . A convex lens is in contact with a concave lens . The magnitude of the ratio of their focal lengths is 2/3 . Their equivalent focal length is 3o cm . What are their individual focal lengths ?

- (a) – 15 , 10
- (b) – 10 , 15
- (c) 75 , 50
- (d) – 75 , 50

4 . A container is filled with water ( μ = 1.33 ) upto a height of 33.25 cm . A convex mirror is placed 15 cm above the water level and the image of an object is placed at the bottom is formed 25 cm below the water level . Focal length of the mirror is –

- (a) 15 cm
- (b) 20 cm
- (c) – 18.31 cm
- (d) 10 cm

5 . A short linear object of length b lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror . The size of the image is approximately equal to

- (a) b ( u – f / f )
^{½} - (b) b ( b / b – f )
^{½} - (c) b ( u – f / f )
- (d) b ( f / u – f ) ²

6 . A thin prism P1 with angle 4° and made from glass of refractive index 1.54 is combined with another thin prism P2 made from glass of refractive index 1.72 to produce dispersion without deviation . The angle of the prism P2 is –

- (a) 5.33°
- (b) 4°
- (c) 3°
- (d) 2.6°

7 . A ray enters a glass slab at an angle α from air where the refractive index varies along the slab as μ = μ_{0}– k r² , where r is the distance measured along the normal and μ_{0} , k are positive constants . If the glass slab is sufficiently thick , how far along the normal will the ray go before it is reflected back ?

- (a) μ
_{0}– sin θ / k - (b) μ
_{0}+ sin θ / k - (c) √ ( μ
_{0}– sin θ / k ) - (d) √ ( μ
_{0}+ sin θ / k )

8 . A bird is flying up at an angle sin^{-1} ( 3/5 ) with the horizontal. A fish in a pond looks at the bird when the bird is vertically above it . The angle at which the bird appears to fly , to the fish is – ( n_{water}= 4/3 )

- (a) sin
^{-1}( 3/5 ) - (b) sin
^{-1}( 4/5 ) - (c) 45°
- (d) sin
^{-1}( 9/16 )

9 . A glass sphere of radius 5.0 cm and refractive index 1.6 is used to construct a paperweight by slicing through the sphere on a plane that is 2.0 cm from the centre of the sphere . Moreover , this plane is perpendicular to a radius of the sphere that passes through the centre of the circle formed by the intersection of the plane and the sphere . The paperweight is placed on a table and viewed from directly above by an observer who is 8.0 cm from the tabletop. When viewed through the paperweight , how far away does the table top appear to the observer ?

- (a) 7.42 cm
- (b) 6.5 cm
- (c) 3 cm
- (d) 4.44 cm

10 . A fish rises up vertically in a pond with a speed of 4 cm/s and notices a bird which is diving downwards towards the fish. The speed of the bird appears to be 16 cm/s , to the fish . If the refractive index of the water is 4/3 , the actual velocity of the bird is –

- (a) 4 cm/s
- (b) 9 cm/s
- (c) 16 cm/s
- (d) 6.2 cm/s