A ray oflight is incident on a surface of glass slab at an angle 45°. If the lateral shift produced per unit thickness is $\frac{1}{\sqrt{3}}$ m, the angle of refraction produced is

• ${\tan }^{-1} \left(\frac{\sqrt{3}}{2}\right)$

• ${\tan }^{-1} \left(1 - \sqrt{\frac{2}{3}}\right)$

• ${\sin }^{-1} \left(1 - \sqrt{\frac{2}{3}}\right)$

• ${\tan }^{-1} \left(\sqrt{\frac{2}{\sqrt{3} - 1}}\right)$

Two luminous point sources separated by a certain distance are at 10 km from an observer. If the aperture of his eye is 2.5 × 10^-3 m and the wavelength of light used is 500 nm, the distance of separation between the point sources just seen to be resolved is

• 12.2 m

• 24.2 m

• 2.44 m

• 1.22 m

The angle of minimum deviation for an incident light ray on an equilateral prism is equal to its refracting angle. The refractive index of its material is

• $\frac{1}{\sqrt{2}}$

• $\sqrt{3}$

• $\frac{\sqrt{3}}{2}$

• $\frac{3}{2}$

A parallel beam of light is incident on a converging lens parallel to its principal axis. As one moves away from the lens on the other side of the principal axis, the intensity of light

• first decreases and then increases

• continuously increases

• continuously decreases

• first increases and then decreases

A ray of light is incident on a plane mirror at an angle of 60°. The angle of deviation produced by the mirror is

• 120°

• 30°

• 60°

• 90°

A point object O is placed in front of a glass rod having spherical end of radius of curvature 30 cm. The image would be formed at

• 30 cm left

• infinity

• 1 cm to the right

• 18 cm to the left

A, B and C are the parallel sided transparent media of refractive indices n₁ n₂ and n₃ respectively. They are arranged as shown in the figure. A ray is incident at an angle i on the surface of separation of A and B which is as shown in the figure. After the refraction into the medium B, the ray grazes the surface of separation of the madia B and C. Then, sin i equals to

• $\frac{{\mathrm{n}}_3}{{\mathrm{n}}_1}$

• $\frac{{\mathrm{n}}_1}{{\mathrm{n}}_3}$

• $\frac{{\mathrm{n}}_2}{{\mathrm{n}}_3}$

• $\frac{{\mathrm{n}}_1}{{\mathrm{n}}_2}$

A boat has green light of wavelength λ = 500 nm on the mast. What wavelength would be measured and what colour would be observed for this light as seen by a diver submerged in water by the side of the boat ? Given, ${\mathrm{n}}_{\mathrm{w}} = \frac{4}{3}$.

• Green of wavelength 376 nm

• Red of wavelength 665 nm

• Green of wavelength 500 nm

• Blue of wavelength 376 nm

129.

Two beams of red and violet colours are made to pass separately through a prism of A = 60°. In the minimum deviation position, the angle of refraction inside the prism will be

• greater for red colour

• equal but not 30° for both the colours

• greater for violet colour

• 30° for both the colours

A plano-convex lens is made of refractive index of 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is

• 400 cm

• 200 cm

• 100 cm

• 50 cm