Lateral Displacement

Q. ${}^{\prime }{n}^{\prime }$ transparent slabs of refractive index $1.5$ each having thickness $1\text{cm},2\text{cm},...n\text{cm}$ are arranged one over the other. A point object is seen through this combination from top with perpendicular light. If the shift of the object by combination is $5\text{cm}$. Then the value of ${}^{\prime }{n}^{\prime }$ is

Q. Two parallel rays are travelling in a medium of refractive index ${\mu }_1=\frac{4}{3}$. One of the rays passes through a parallel glass slab of thickness t and refractive index ${\mu }_2=\frac{3}{2}$. The path difference between the two rays due to the glass slab will be

1. $\frac{t}{8}$
2. $\frac{4t}{3}$
3. $\frac{3t}{2}$
4. $\frac{t}{6}$

Q. A beam of light is converging towards a point I on a screen. A plane glass plate whose thickness in the direction of the beam = t, refractive index =$\mu$ , is introduced in the path of the beam. The convergence point is shifted by

1. 
2. 
3. 
4. 

Q.

A diverging beam of light from a point source S having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

1. Zero

2. a

3. 

4. 

Q. A ray of light is incident on one face of a transparent slab of thickness $15\text{cm}$. The angle of incidence is ${60}^{\circ }$. If the lateral displacement of the ray on emerging from the parallel plane is $5\sqrt{3}\text{cm}$, the refractive index of the material of the slab is

1. None
2. $1.414$
3. $1.532$
4. $1.732$

Q. A slab of glass of thickness of $3$ units and refractive index $\sqrt{3}$ is surrounded by vacuum and is placed as shown. A light ray is incident at the point $(2,5\sqrt{3})$ as shown. The point where the ray will cut the $X-$ axis is:

1. $(6,0)$
2. $(5+\sqrt{3},0)$
3. $(9,0)$
4. $(8,0)$

Q. A beam of light is converging towards a point $L$. A plane parallel plate of glass of thickness $t$, refractive index $\mu$ is introduced in the path of the beam. The convergent point is shifted by :

1. $t(1-\frac{1}{\mu })away$
2. $t(1+\frac{1}{\mu })away$
3. $t(1-\frac{1}{\mu })nearer$
4. $t(1+\frac{1}{\mu })nearer$

Q. An equiconvex lens has a power of 5 deoptre. IF it is made of glass of refractive index 1.5. then radius of curvature of its each surface will be?

1. $\infty$
2. 20 cm
3. 10 cm
4. 40 cm

Q. A monochromatic light passes through a glass slab $(\mu =\frac{3}{2})$ a thickness $90cm$ in time $t_1$. If it takes $t_2$ to travel the same distance through water $(\mu =\frac{4}{3})$. The value of $(t_1-t_2)$ is :

1. $5\times {10}^{-10}s$
2. $5\times {10}^{-8}s$
3. $2.5\times {10}^{-10}s$
4. $2.5\times {10}^{-8}s$

Q. A monochromatic ray of light is incident on the surface of a glass slab of thickness $8cm$, making and angle ${30}^{\circ }$ with the surface. The lateral displacement of the ray of light will be $({\mu }_g=\sqrt{3})$.

1. $5.62cm$
2. $4.62cm$
3. $3.62cm$
4. $8cm$