A liquid of refractive index \(\frac{4}{3}\) is placed between two identical planoconvex-lenses touching each other at their spherical surfaces of radius \(R\). If the refractive index of the lens is \(1.50\), then the lens behaves as:

1.	a convergent with power \(P=\frac{1}{3 R}\)
2.	a convergent with power \(P=\frac{1}{6 R}\)
3.	a divergent with power \(P=\frac{1}{3 R}\)
4.	a divergent with power \(P=\frac{1}{6 R}\)

The thickness of a plano-convex glass lens in the middle is 1.5 cm. Viewing from the flat side the thickness of the lens at the centre will appear (refractive index of glass is 1.5) to be

1.  1.5 cm

2.  1.0 cm

3.  2 cm

4.  0.5 cm

A ray of light incident on an equilateral prism at an angle of incidence i. The deviation produced by prism will be maximum when angle i is [take ${\mu }_{glass}=2$]

(1) 30$°$

(2) 45$°$

(3) 60$°$

(4) 90$°$

A lens of focal length \(f_{a}\) in air consists of a glass of refractive index \(\mu_{g}.\) If \(f_{l}\) is its focal length in a liquid of refractive index \(\mu_{l},\) then for \(\mu_{l}=\mu_{g}\)
1. \(f_{l}=0\)
2. \(\infty >f_{l}>f_{a}\)
3. \(0<f_{l}<f_{a}\)
4. \(f_{l}=\infty \)

If four convex lenses, given to you have focal lengths $f_1<f_2<f_3<f_4$, then which of the following combination will you prefer to form a compound microscope?

(1) $f_1$ as objective and $f_4$ as eye-lens

(2) $f_1$ as objective and $f_2$ as eye-lens

(3) $f_4$ as objective and $f_1$ as eye-lens

(4) $f_2$ as objective and $f_3$ as eye-lens

A light ray is incident on a prism of refracting angle $30°$. The refractive index of prism is $\sqrt{2}$, then for what value of angle of incidence, the ray will retrace its path?

1.  $30°$

2.  $45°$

3.  $37°$

4.  $60°$

The ratio of the velocity of light in a medium to the velocity of light in a vacuum is $\frac{4}{5}$. If the ray of light is emerging from this medium into the air, then the critical angle for this interface of medium and air will be:

(1) 30$°$

(2) 37$°$

(3) 53$°$

(4) 45$°$

If light ray is incident normally on face AB of a part of a prism, then for no emergent ray from second face AC [$\mu \to$refractive index of glass of prism]

(1) $\mu =\frac{2}{\sqrt{3}}$

(2) $\mu >\frac{2}{\sqrt{3}}$

(3) $\mu <\frac{2}{\sqrt{3}}$

(4) $\mu$ can have any value

A plane mirror is fixed in YZ-plane at x = 0. The velocity of a moving object is $\overrightarrow{v_0}=3\hat{i}+6\hat{j}+4\hat{k}$. The velocity of the image relative to a stationary observer will be:

1.  $3\hat{i}-6\hat{j}-4\hat{k}$

2.  $3\hat{i}-6\hat{j}+4\hat{k}$

3.  $-3\hat{i}+6\hat{j}+4\hat{k}$

4.  $-3\hat{i}-6\hat{j}-4\hat{k}$

If there is no emergent light through a prism of refracting angle \(60^{\circ},\) whatever may be the angle of incidence, then the minimum value of the refractive index of the material of the prism is: