Embibe Experts Solutions for Chapter: Wave Optics, Exercise 3: Exercise-3

Consider interference between two sources of intensity $I$ and $4I$. Find out resultant intensity where phase difference is

$\frac{\pi }{4}$ 

Express all your answers in the form $nI$ where $n$ is real number up to two decimal places. Find $n$.

Consider interference between two sources of intensity $I$ and $4I$. Find out resultant intensity where phase difference is $\pi$

Express all your answers in the form $nI$ where $n$ is real number up to two decimal places. Find $n$.

Consider interference between two sources of intensity $I$ and $4I$. Find out resultant intensity where phase difference is $4\pi$

Express all your answers in the form $nI$ where $n$ is real number up to two decimal places. Find $n$.

A ray of light of intensity I is incident on a parallel glass-slab at a point $A$ as shown in figure. It undergoes partial reflection and refraction. At each reflection $20\%$ of incident energy is refracted. The rays $AB$ and $A^{\text{'}}{B}^{\text{'}}$ undergo interference. The ratio of $\frac{I_{\max }}{I_{\min }}$ is $x:1$. Write the value of $x$.

In a double-slit experiment, fringes are produced using light of wavelength $4800 \stackrel{°}{\mathrm{A}}$. One slit is covered by a thin plate of glass of refractive index $1.4$ and the other slit by another plate of glass of double thickness and of refractive index $1.7$. On doing so, the central bright fringe shifts to a position originally occupied by the fifth bright fringe from the centre. Find the thickness of the second plates (in $\mu \mathrm{m}$)

In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by $5\times {10}^{-2} \mathrm{m}$ towards the slits, the change in fringe width is $3\times {10}^{-5} \mathrm{m}$. If the distance between the slits is ${10}^{-3} \mathrm{m}$, calculate the wavelength of the light used (in $\stackrel{°}{\mathrm{A}}$).

A thin glass plate of thickness $t$ and refractive index $\mu$ is inserted between screen and one of the slits in a Young's experiment. If the intensity at the centre of the screen is $I$, what was the intensity at the same point prior to the introduction of the sheet.
Express your answer as $I{\cos }^2\left[\frac{k(\mu -1)t}{\lambda }\right]$ and find the value of $k$.

(Take $\pi =3.14$)

Light of wavelength $520 \mathrm{nm}$ passing through a double slit, produces interference pattern of relative intensity versus deflection angle $\theta$ as shown in the figure. Find the separation $d$ between the slits. If your answer is $x\times {10}^{-2} \mathrm{mm}$, fill the value of $x$.