Download App

Wave Optics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsWave Optics4 Marks
Question
In Young's double $-$ slit experiment using monochromatic light of wavelength $\lambda,$ the intensity of light at a point on the screen where the path difference is $\lambda$ is $1$ . What is the intensity of light at a point where the path difference is $\lambda / 3$ ?
✓

Answer

Data : $\Delta I_1=\lambda, I_1=1, \Delta I_2=\lambda / 3$
We assume that light waves coming out of the two slits are of equal intensity lo.
Then at a point in the interference pattern where the phase difference between the interfering waves is $\varphi$, the resultant intensity is,
$1=2 l_0(1+\cos \varphi)$
Phase difference $(\varphi)=\frac{2 \pi}{\lambda} \times$ path difference $(\Delta \mid)$
$\therefore$ For $\Delta l_1-\lambda \phi_1=\frac{2 t}{i} \times \lambda=2 \approx$ rad
$\therefore I_1 =2 l_0\left(1+\cos \phi_1\right)=2 I_9(1+\cos 2 \pi)$
$ =2 l_0(1+1)=4 I_0$
$\therefore l_0 =\frac{l_3}{4}=\frac{l}{4}$
For, $\Delta l_2=\lambda / 3, \phi_2=\frac{2 \pi}{2} \times \frac{\lambda}{3}=\frac{2 \pi}{3} rad$
$\cos \frac{2 \pi}{3}=\cos 12 O^{\circ}=-\sin 30^{\circ}=-\frac{1}{2}$
$\therefore I_2=2 I_0\left(1+\cos \phi_2\right)=2 \times \frac{1}{4}\left(1+\cos \frac{2 \pi}{3}\right)$
$-2 \times \frac{I}{4}\left(1-\frac{1}{2}\right)=2 \times \frac{1}{4} \times \frac{1}{2}=\frac{I}{4}$
$\therefore$ A The intensity of light at a point where the path difference is $N / 3$ is $\lambda / 4$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Answer the following in Detail" from Wave Optics→Wave Optics — all question types→Physics STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

We have mentioned about ‘static friction’ between road and tyres. Why is it static friction? What about kinetic friction between road and tyres?
→
What is a magnetically hard material?
→
With a neat diagram, describe a spring-and-block oscillator.
→
Determine the series limit of Balmer, Paschen and Bracket series, given the limit for Lyman series is $912\ Å.$
→
What is the electric potential energy of the following charge configuration? Take $q_1=+1 \times 10^{-8} C _1 q _2=-2 \times 10^{-8} C , q _3=+3 \times 10^{-8} C , q _4=2 \times 10^{-8} C$ and $a =1 m$. Assume the charges to be in vacuum.
Image
→
Why is a resistance connected in series with a Zener diode when used in a circuit?
→
During a stunt, a cyclist (considered to be a particle) is undertaking horizontal circles inside a cylindrical well of radius 6.05 m. If the necessary friction coefficient is 0.5, how much minimum speed should the stunt artist maintain? Mass of the artist is 50 kg. If she/he increases the speed by 20%, how much will the force of friction be?
$\left[\right.$
→
A load of $100 g$ increases the length of a light spring by $10 cm$. Find the period of its linear SHM if it is allowed to oscillate freely in the vertical direction. What will be the period if the load is increased to $400 g$ ? $\left[ g =9.8 m / s ^2\right.]$
→
Using the expression for the radius of orbit for the Hydrogen atom, show that the linear speed varies inversely to the principal quantum number $n$ the angular speed varies inversely to the cube of principal quantum number $n.$
→
What do you mean by a logic gate, a truth table and a Boolean expression?
→