(A) The lateral shift $d$ is given by the formula: $d = \frac{t \sin(i-r)}{\cos r}$.Given the refractive index $n = \frac{\sin i}{\sin r}$.For small a

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) The lateral shift $d$ is given by the formula: $d = \frac{t \sin(i-r)}{\cos r}$.Given the refractive index $n = \frac{\sin i}{\sin r}$.For small angles,$\sin i \approx i$,$\sin r \approx r$,$\cos i \approx 1$,and $\cos r \approx 1$.Thus,$n = \frac{i}{r} \implies r = \frac{i}{n}$.Substituting $i = \theta$ and $r = \frac{\theta}{n}$ into the lateral shift formula:$d = t \frac{\sin(\theta - \frac{\theta}{n})}{\cos(\frac{\theta}{n})} \approx t \frac{\theta - \frac{\theta}{n}}{1} = t \theta \left(1 - \frac{1}{n}\right) = \frac{t \theta (n-1)}{n}$.

Class 12 Physics Ray Optics and Optical Instruments Refraction through Plane Surface and Glass Slab

$A$ ray of light is incident on a parallel slab of thickness $t$ and refractive index $n$. If the angle of incidence $\theta$ is small,then the lateral displacement between the incident and emergent ray will be:

A
$\frac{t \theta (n-1)}{n}$
B
$\frac{t \theta}{n}$
C
$\frac{t \theta n}{n-1}$
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Ray Optics and Optical Instruments

Subtopic

Refraction through Plane Surface and Glass Slab

$A$ glass slab of thickness $20\, cm$ and refractive index $1.5$ is placed in front of a plane mirror. An object is placed at a distance of $40\, cm$ from the mirror in air. The position of the final image with respect to the mirror will be at a distance of:

Difficult

View Solution

$A$ large glass slab $\left( \mu = \frac{5}{3} \right)$ of thickness $8 \, cm$ is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R \, cm$. What is the value of $R$? ....... $cm$

Medium

View Solution

$A$ bubble in a glass slab $(\mu = 1.5)$ when viewed from one side appears at $5 \ cm$ and from the other side appears at $2 \ cm$. The thickness of the slab is .... $cm$.

MediumAIPMT 2000

View Solution

$A$ microscope is focussed on a coin lying at the bottom of a beaker. The microscope is now raised by $1 \,cm$. To what depth should water be poured into the beaker so that the coin is again in focus is ........ $cm$ (The refractive index of water is $\frac{4}{3}$ )

Easy

View Solution

Three immiscible liquids of densities $d_1 > d_2 > d_3$ and refractive indices $\mu_1 > \mu_2 > \mu_3$ are put in a beaker. The height of each liquid column is $\frac{h}{3}$. $A$ dot is made at the bottom of the beaker. For near normal vision,find the apparent depth of the dot.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ ray of light is incident on a parallel slab of thickness $t$ and refractive index $n$. If the angle of incidence $\theta$ is small,then the lateral displacement between the incident and emergent ray will be:

Similar Questions

$A$ glass slab of thickness $20\, cm$ and refractive index $1.5$ is placed in front of a plane mirror. An object is placed at a distance of $40\, cm$ from the mirror in air. The position of the final image with respect to the mirror will be at a distance of:

$A$ large glass slab $\left( \mu = \frac{5}{3} \right)$ of thickness $8 \, cm$ is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R \, cm$. What is the value of $R$? ....... $cm$

$A$ bubble in a glass slab $(\mu = 1.5)$ when viewed from one side appears at $5 \ cm$ and from the other side appears at $2 \ cm$. The thickness of the slab is .... $cm$.

$A$ microscope is focussed on a coin lying at the bottom of a beaker. The microscope is now raised by $1 \,cm$. To what depth should water be poured into the beaker so that the coin is again in focus is ........ $cm$ (The refractive index of water is $\frac{4}{3}$ )

Three immiscible liquids of densities $d_1 > d_2 > d_3$ and refractive indices $\mu_1 > \mu_2 > \mu_3$ are put in a beaker. The height of each liquid column is $\frac{h}{3}$. $A$ dot is made at the bottom of the beaker. For near normal vision,find the apparent depth of the dot.

Vedclass Test Series

Exam Paper Generator

Online Exam Module