Consider the situation given in the figure.
Question: Consider the situation given in the figure. The two slits $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ placed symmetrically around the central line are illuminated by a monochromatic light of wavelength $\lambda$. The separation between the slits is $d$. The light transmitted by the slits falls on a screen $\Sigma_{1}$ placed at a distance $D$ from the slits. The slit $S_{3}$ is at the central line and the slit $S_{4}$ is at a distance $z$ from $S_{3}$ Another screen $\Sigma_{2}$ is placed a ...
Read More →The linewidth of a bright fringe is sometimes defined
Question: The linewidth of a bright fringe is sometimes defined as the separation between the points on the two sides of the central line where the intensity falls to half the maximum. Find the linewidth of a bright fringe in a Young's double slit experiment in terms of $\lambda, d$ and D where the symbols have their usual meanings. Solution:...
Read More →In a Young's double slit experiment
Question: In a Young's double slit experiment $\lambda=500 \mathrm{~nm}, \mathrm{~d}=1.0 \mathrm{~mm}$ and $D=1.0 \mathrm{~m}$. Find the minimum distance from the central maximum for which the intensity is half of the maximum intensity. Solution:...
Read More →In a Young's double slit interference experiment
Question: In a Young's double slit interference experiment the fringe pattern is observed on a screen placed at a distance $D$ from the slits. The slits are separated by a distance $d$ and are illuminated by monochromatic light of wavelength $\lambda$. Find the distance from the central point where the intensity falls to (a) half the maximum, (b) one fourth of the maximum. Solution:...
Read More →In a Young's double slit experiment, the separation between
Question: In a Young's double slit experiment, the separation between the slits $=2.0 \mathrm{~mm}$, the wavelength of the light=600 $\mathrm{nm}$ and the distance of the screen from the slits $=2.0 \mathrm{~m}$. If the intensity at the centre of the central maximum is $0.20 \mathrm{~W} / \mathrm{m}^{2}$, what will be the intensity at a point $0.5 \mathrm{~cm}$ away from this centre along the width of the fringes? Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sin ^{-1}(\cos x)$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\cot ^{-1} x^{3}$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\log \left(\tan ^{-1} x\right)$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\cot ^{-1}\left(e^{x}\right)$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\tan ^{-1}(\log x)$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sin ^{-1} \frac{x}{a}$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sec ^{-1} \sqrt{x}$ Solution:...
Read More →Figure shows equidistant slits being illuminated by a monochromatic parallel beam of light.
Question: Figure shows equidistant slits being illuminated by a monochromatic parallel beam of light. Let $B P_{0}-A P_{0}=\lambda / 3$ and $\mathrm{D}\lambda$ (a) Show that in this case $=\sqrt{2 \lambda D / 3}$ (b) Show that the intensity at $P_{0}$ slits individually. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\tan ^{-1} x^{2}$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : Solution:...
Read More →Two coherent point sources S1 and S2 vibrating in phase emit light of wavelength λ.
Question: Two coherent point sources $S_{1}$ and $S_{2}$ vibrating in phase emit light of wavelength $\lambda$. The separation between the sources is 2 $\lambda$. Consider a line passing through $S_{2}$ and perpendicular to the line $S_{1}, S_{2}$. What is the smallest distance from $S_{2}$ where a minimum of intensity occurs? Solution:...
Read More →Consider the arrangement shown in figure.
Question: Consider the arrangement shown in figure. The distance $D$ is large compared to the separation $d$ between the slits. (a) Find the minimum value of $d$ so that there is a dark fringe at $O$. (b) Suppose $d$ has this value. Find the distance $x$ at which the next bright fringe is formed. (c) Find the fringe-width. Solution:...
Read More →White coherent light (400 nm-700 nm) is sent through the slits of a Young's double slit experiment.
Question: White coherent light ( $400 \mathrm{~nm}-700 \mathrm{~nm}$ ) is sent through the slits of a Young's double slit experiment. The separation between the slits is $0.5 \mathrm{~mm}$ and the screen is $50 \mathrm{~cm}$ away from the slits. There is a hole in the screen at a point $1.0 \mathrm{~mm}$ away (along the width of the fringes) from the central line. (a) Which wavelength(s) will be absent in the light coming from the hole? (b) Which wavelength(s) will have a strong intensity? Solut...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $e^{x \cos x}$ Solution:...
Read More →A double slit S1-S2 is illuminated by a coherent light of wavelength λ.
Question: A double slit $\mathrm{S}_{1}-\mathrm{S}_{2}$ is illuminated by a coherent light of wavelength $\lambda$. The slits are separated by a distance $\mathrm{d}$. A plane mirror is placed in front of the double slit at a distance $D_{1}$ from it and a screen $\Sigma$ is placed behind the double slit at a distance $D_{2}$ from it. The screen $\Sigma$ receives only the light reflected by the mirror. Find the fringe-width of the interference pattern on the screen. Solution:...
Read More →A long narrow horizontal slit is placed
Question: A long narrow horizontal slit is placed $1 \mathrm{~mm}$ above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen $1.0 \mathrm{~m}$ away from the slit. Find the fringe-width if the light used has a wavelength of $700 \mathrm{~nm}$. Solution:...
Read More →A narrow slit S transmitting light of wavelength
Question: A narrow slit $S$ transmitting light of wavelength $\lambda$ is placed a distance $d$ above a large plane mirror as shown in figure. The light coming directly from the slit and that coming after the reflection interface at a screen $\Sigma$ placed at a distance D from the slit. (a) What will be the intensity at a point just above the mirror, i.e., just above 0 ? (b) At what distance from 0 does the first maximum occur? Solution:...
Read More →A parallel beam of monochromatic light is used in a Young's
Question: A parallel beam of monochromatic light is used in a Young's double slit experiment. The slits are separated by a distance d and the screen is placed parallel to the plane of the slits. Show that if the incident beam makes an angle $\theta=\sin ^{-1}\left(\frac{\lambda}{2 d}\right)$ with the normal to the plane of the slits, there will be a dark fringe at the centre ${ }^{P_{0}}$ of the pattern. Solution:...
Read More →A Young's double slit apparatus has slits separated
Question: A Young's double slit apparatus has slits separated by $0.28 \mathrm{~mm}$ and a screen $48 \mathrm{~cm}$ away from the slits. The whole apparatus is immersed in water and the slits are illuminated by the red light $(\lambda=700 \mathrm{~nm}$ in vaccum). Find the fringe-width of the pattern formed on the screen. Solution:...
Read More →A thin paper of thickness 0.02 mm having a refractive index 1.45
Question: A thin paper of thickness $0.02 \mathrm{~mm}$ having a refractive index $1.45$ is pasted across one of the slits in a Young's double slit experiment. The paper transmits $4 / 9$ of the light energy falling on it. (a) Find the ratio of the maximum intensity to the minimum intensity in the fringe pattern. (b) How many fringes will cross through the centre if an identical paper piece is pasted on the other slit also? The wavelength of the light used is $600 \mathrm{~nm}$. Solution:...
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