Maxima in Diffraction

Q. What is the minimum thickness of a soap film needed for constructive interference in reflected light, if the light incident on film is of wavelength $900\text{nm}$ ?
Refractive index of film is $1.5$.

1. $100\text{nm}$
2. $150\text{nm}$
3. $200\text{nm}$
4. $250\text{nm}$

Q. The figure shows a Young's double slit experiental setup. It is observed that when a thin transparent sheet of thickness $t$ and refractive index $\mu$ is put in front of one of the slits, the central maximum gets shifted by a distance equal to $n$ fringe widths. If the wavelength of light used is $\lambda$, $t$ will be

1. None of the above
2. $\frac{nD\lambda }{a(\mu -1)}$
3. $\frac{D\lambda }{a(\mu -1)}$
4. $\frac{2nD\lambda }{a(\mu -1)}$
5. $\frac{2D\lambda }{a(\mu -1)}$

Q. $\text{Assertion:}$ In the figure shown, zero order maxima will lie above point $O$.
$\text{Reason:}$ Zero order maxima normally means a point where path difference is zero.

1. Both the Assertion and Reason are true, and the Reason is the correct explanation of the Assertion.
2. Both the Assertion and Reason are true, but Reason is not the correct explanation of Assertion.
3. The Assertion is true, but the Reason is false.
4. The Assertion is false, but the Reason is true.

Q. A glass plate of refractive index ${\mu }_1=1.5$ is coated with a thin layer of thickness $t$ and refractive index ${\mu }_2=\mathrm{1.8.}$ Light of wavelength $\lambda$ travelling in air is incident normally on the layer. It is partly reflected at the upper and lower surfaces of the layer, and the two reflected rays interfere. If $\lambda =648\text{nm}$ obtain the least, value of $t$ for which rays interfere constructively.(in $\text{nm}$) . (integers only)

Q. In a Young's double slit experiment for interference of light, the slits are $0.2\text{cm}$ apart and are illuminated by yellow light$(\lambda =600\text{nm})$. What would be the fringe width on a screen placed $1\text{m}$ from the plane of slits if the whole system is immersed in water of refractive index $\frac{4}{3}.$

1. $2.25\text{mm}$
2. $0.125\text{mm}$
3. $0.225\text{mm}$
4. $1.25\text{mm}$

Q. A parallel beam of sodium light of wavelength $6000\mathring{A}$ is incident on a thin glass plate of $\mu =1.5$, such that the angle of refraction in the plate is ${60}^{\circ }$. The smallest thickness of the plate which will make it appear dark by reflected light is

1. $40\mathring{A}$
2. $4\mathring{A}$
3. $400\mathring{A}$
4. $4000\mathring{A}$

Q.

A plane wave of wavelength $6250\AA$is incident normally on a slit of width $2\times {10}^{-2}cm$. The width of the principal maximum on a screen distant $50cm$ will be

1. $312.5\times {10}^{-3}cm$

2. $31.25\times {10}^{-3}cm$

3. $312cm$

4. $312.5\times {10}^{-3}mm$

Q. A screen is at a distance $D=80\text{cm}$ from a diaphragm having two narrow slits $S_1$ and $S_2$ which are $d=2\text{mm}$ apart. Slit $S_1$ is covered by a transparent sheet of thickness $t_1=2.5\mu \text{m}$ and slit $S_2$ is covered by another sheet of thickness $t_2=1.25\mu \text{m}$ as shown in figure


Both sheets are made of same material having refractive index $\mu =1.40$. Water is filled in the space between diaphragm and screen. A monochromatic light beam of wavelength $\lambda =5000\dot{\text{A}}$ is incident normally on the diaphragm. Assuming intensity of beam to be uniform, calculate ratio of intensity at $C$ to the maximum intensity of interference pattern obtained on the screen $({\mu }_w=\frac{4}{3})$.

1. $\frac{4}{3}$
2. $\frac{2}{3}$
3. $\frac{3}{4}$
4. $\frac{1}{3}$

Q. Electromagnetic wave of intensity $1400{\text{W/m}}^2$ falls on metal surface on area $1.5{\text{m}}^2$ is completely absorbed by it. Find out the force exerted by the beam.

1. $14\times {10}^{-5}\text{N}$
2. $14\times {10}^{-6}\text{N}$
3. $7\times {10}^{-5}\text{N}$
4. $7\times {10}^{-6}\text{N}$

Q. Consider a case of thin film interference as shown. Thickness of film is equal to wavelength of light in ${\mu }_2$

1. Reflected light will be maxima if ${\mu }_1<{\mu }_2<{\mu }_3$
2. Reflected light will be maxima if ${\mu }_1<{\mu }_2>{\mu }_3$
3. Transmitted light will be maxima if ${\mu }_1<{\mu }_2>{\mu }_3$
4. Transmitted light will be maxima if ${\mu }_1>{\mu }_2>{\mu }_3$

Q. A point source $S$ emits light of wavelength $600\text{nm}.$ It is placed at a very small distance from a flat reflecting mirror $\text{AB}$. Interference fringes are observed on the screen placed parallel to the reflecting surface at very large distance $D$ from it. The ratio of minimum to maximum intensities in the interference fringes formed near the point $\text{P}$ is $\frac{1}{6}.$ If the ratio of intensity of the reflected light to the intensity of incident light is $0.09k.$ The value of $k$ is

1. $1$
2. $2$
3. $3$
4. $4$

Q. A monochromatic light of $\lambda =6000\mathring{\text{A}}$ is incident on the slits. The interference pattern is observed on a screen and central maxima is formed at point $O$. A thin glass plate of thickness $0.4\mu \text{m}$ and refractive index $1.5$ is placed in front of one of the slits. If the intensity at point $O$ is $I_0$ initially, what will be the intensity at $O$ after placing the glass plate?

1. $I_0$
2. $\frac{I_0}{2}$
3. $\frac{I_0}{4}$
4. $\frac{I_0}{\sqrt{2}}$

Q. If wavelengths $4500\mathring{A}$ and $6000\mathring{A}$ are found to be missing in the reflected spectrum in thin air film interference, the thickness of the film for normal incidence is nearly

1. $9000\mathring{A}$
2. $10500\mathring{A}$
3. $5250\mathring{A}$
4. $4240\mathring{A}$

Q. A transparent film of thickness $5\mu \text{m}$ and refractive index $1.4$ is placed in front of the lower slit as shown in the diagram. As a result, the interference pattern shifts through a distance $2\text{mm}$. Find the order of the bright/dark band forming at point $O$ after placing the film. The wavelength of the monochromatic light used is $5000\mathring{\text{A}}$.

1. Second dark fringe
2. Second bright fringe
3. Fourth bright fringe
4. Fourth dark fringe

Q. The minimum thickness of a soap film needed for constructive interference in reflected light, if the light incident on film is of wavelength $900\text{nm}$ is $x\text{nm}$. Find the value of $x$

Refractive index of film is $1.5$.

Q. $P_1\text{and}{P}_2$ are transparent plates having equal thickness $20\mu \text{m}$ and refractive indices ${\mu }_1=1.6\text{and}{\mu }_2=1.5$. $P_2$ transmits $75\text{\%}$ whereas $P_2$ transmits $50\text{\%}$ of incident energy. The wavelength of the monochromatic source is $4000\dot{\text{A}}$. Without $P_1\text{and}{P}_2$, the intensity at $O$ is $I_0=4I$. The intensity at $O$ after placing $P_1\text{and}{P}_2$:

$(S_1\text{and}{S}_2\text{are identical slits},I\text{be incident intensity})$

1. $\frac{5I}{4}$
2. $\frac{5I}{4}+I\sqrt{\frac{3}{2}}$
3. $\frac{I}{2}+\frac{5I\sqrt{3}}{4}$
4. $\frac{\sqrt{3}I}{2}$

Q. What is the minimum thickness of a soap bubble needed for constructive interference of reflected light if the light incident on the film is of wavelength $900\text{nm}$ and refractive index of the film is $\mathrm{1.5.}$

1. $100\text{nm}$
2. $150\text{nm}$
3. $200\text{nm}$
4. $250\text{nm}$

Q. A glass plate of refractive index ${\mu }_1=1.5$ is coated with a thin layer of thickness $t$ and refractive index ${\mu }_2=\mathrm{1.8.}$ Light of wavelength $\lambda$ travelling in air is incident normally on the layer. It is partly reflected at the upper and lower surfaces of the layer, and the two reflected rays interfere. If $\lambda =648\text{nm}$ obtain the least, value of $t$ for which rays interfere constructively.(in $\text{nm}$) . (integers only)

Q. In Young's double-slit experiment, the point source $S$ is placed slightly off the central axis, as shown in figure. If $\lambda =500\text{nm}$, then match the following

Column $\left(\text{I}\right)$	Column $\left(\text{II}\right)$
$\left(A\right)$ Nature and order of interference at point $P$, $OP=10\text{mm}$	$1.$ Bright fringe of order $80$
$\left(B\right)$ Nature and order of interference at point $O$	$2.$ Bright fringe of order $262$
$\left(C\right)$ If a transparent paper (refractive index $\mu =1.45$) of thickness $t=0.02\text{mm}$ is pasted on $S_1$, i.e., one of the slits, the nature and order of interference at point $P$	$3.$ Bright fringe of order $62$
$\left(D\right)$ After inserting the transparent paper in front of Slit $S_1$, the nature and order of interference at $O$.	$4.$ Bright fringe of order $280$

1. $A\to 1;B\to 3;C\to 4;D\to 2$
2. $A\to 1;B\to 2;C\to 3;D\to 4$
3. $A\to 3;B\to 1;C\to 2;D\to 4$
4. $A\to 4;B\to 1;C\to 2;D\to 3$

Q. The minimum thickness of a soap film needed for constructive interference in reflected light, if the light incident on film is of wavelength $900\text{nm}$ is $x\text{nm}$. Find the value of $x$

Refractive index of film is $1.5$.

Q. In the ideal double-slit experiment , when a glass-plate (refractive index $\mu =1.5$) of thickness $t$ is introduced in the path of one of the interfering beams having wavelength $\left(\lambda \right),$ the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is-

1. $2\lambda$
2. $\frac{2\lambda }{3}$
3. $\frac{\lambda }{3}$
4. $\lambda$

Q. If the coefficient of absorption and transmission of surface are 0.73 and 0.23 respectively, the coefficient of reflection is:

1. 0.96
2. 0.06
3. 0.24
4. 0.04

Q. A point source $S$ emits light of wavelength $600\text{nm}.$ It is placed at a very small distance from a flat reflecting mirror $\text{AB}$. Interference fringes are observed on the screen placed parallel to the reflecting surface at very large distance $D$ from it. The ratio of minimum to maximum intensities in the interference fringes formed near the point $\text{P}$ is $\frac{1}{6}.$ If the ratio of intensity of the reflected light to the intensity of incident light is $0.09k.$ The value of $k$ is (integer only)

Q.

The bright spots (except the central one), we just found the position of, are maxima.

1. True

2. False

Q. What is the minimum thickness of a soap film needed for constructive interference in reflected light, if the light incident on film is of wavelength $900\text{nm}$ ?
Refractive index of film is $1.5$.

1. $100\text{nm}$
2. $150\text{nm}$
3. $200\text{nm}$
4. $250\text{nm}$

Q. When white light is incident normally on an oil film of thickness ${10}^{-4}cm$ and refractive index $1.4$ then the wavelength which will not be seen in the reflected system.

1. $7000\mathring{A}$
2. $4000\mathring{A}$
3. All of the above
4. $5600\mathring{A}$

Q. Blue light of wavelength $480nm$ is most strongly reflected off a thin film of oil on a glass slab when viewed near normal incidence. Assuming that the index of refraction of the oil is $1.2$ and that of the glass is $1.6$, what is the minimum thickness of the oil film (other than zero)?

1. $200nm$
2. $300nm$
3. $100nm$
4. None

Q. For the situation shown in figure, match the entries of Column I with Column II.
Assume thickness of films to be very small compared towavelenght of incident light.

Q. What is the minimum thickness of a soap film needed for constructive interference in reflected light, if the light incident on film is of wavelength $900\text{nm}$ ?
Refractive index of film is $1.5$.

1. $200\text{nm}$
2. $250\text{nm}$
3. $100\text{nm}$
4. $150\text{nm}$

Q. What is the minimum thickness of a soap film needed for constructive interference in reflected light, if the light incident on film is of wavelength $900\text{nm}$ ?
Refractive index of film is $1.5$.

1. $100\text{nm}$
2. $150\text{nm}$
3. $200\text{nm}$
4. $250\text{nm}$