Download App

Wave Optics — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsWave Optics5 Marks
Question
In a Young's double slit experiment using monochromatic light, the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 micron (1 micron = 10-6m) is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the screen and the slits is doubled. It is found that the distance between the successive maxima now is the same as the observed fringe-shift upon the introduction of the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment.
✓

Answer

In the given Young’s double slit experiment,
$\mu=1.6,$ t = 1.964 micron = 1.964 × 10-6m
We know, number of fringes shifted $=\frac{(\mu-1)\text{t}}{\lambda}$
So, the corresponding shift = No.of fringes shifted × fringe width
$=\frac{(\mu-1)\text{t}}{\lambda}\times\frac{\lambda\text{D}}{\text{d}}=\frac{(\mu-1)\text{tD}}{\text{d}}\ ...(1)$
Again, when the distance between the screen and the slits is doubled,
Fringe width $=\frac{\lambda(2\text{D})}{\text{d}}\ ...(2)$
From (1) and (2), $\frac{(\mu-1)\text{tD}}{\text{d}}=\frac{\lambda(2\text{D})}{\text{d}}$
$\Rightarrow\lambda=\frac{(\mu-1)\text{t}}{\lambda}$
$=\frac{(1.6-1)\times(1.964)\times10^{-6}}{2}=589.2\times10^{-9}=589.2\text{nm}.$

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 "5 Marks Questions" from Wave Optics→Wave Optics — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A load resistor of $2\text{k}\Omega$ is connected in the collector branch of an amplifier circuit using a transistor in common-emitter mode. The current gain $\beta=50.$ The input resistance of the transistor is $0.50\text{k}\Omega.$ If the input current is changed by $50\mu\text{A}.$
  1. By what amount does the output voltage change?
  2. By what amount does the input voltage change?
  3. What is the power gain?
→
A beam of monochromatic light of wavelength $\lambda$ ejects photoelectrons from a cesium surface $\big(\Phi=1.9\text{eV}\big).$ These photoelectrons are made to collide with hydrogen atoms in ground state. Find the maximum value of $\lambda$ for which (a) hydrogen atoms may be ionized, (b) hydrogen atoms may get excited from the ground state to the first excited state and (c) the excited hydrogen atoms may emit visible light.
→
Suppose the $19\Omega$ resistor of the previous problem is disconnected. Find the current through P2Q2 in the two situations:
  1. Both the wires move towards right.
  2. If P1Q1 moves towards left but P2Q2 moves towards right.
→
What do you understand by a solenoid? Obtain an expression for magnetic field of a solenoid of infinite length.###Establish a formula for magnetic field on the axis inside of a straight and long solenoid. Show the direction of magnetic field inside it and what is the magnitude of magnetic field outside the solenoid.###Establish a formula for magnetic field inside a long solenoid. Represent produced force lines by diagram.###Write Ampere's circuital law. Obtain an expression for magnetic field on the axis of a very long current carrying solenoid. Draw necessary diagram also.
→
A hollow sphere is released from the top of an inclined plane of inclination $\theta.$
  1. What should be the minimum coefficient of friction between the sphere and the plane to prevent sliding?
  2. Find the kinetic energy of the ball as it moves down a length 1 on the incline if the friction coefficient is half the value calculated in part (a).
→
In the circuit shown in Fig., when the input voltage of the base resistance is 10V, Vbe is zero and Vce is also zero. Find the values of Ib, Ic and β.

→
A particle of mass m and charge q is thrown at a speed u against a uniform electric field E. How much distance will it travel before coming to momentary rest?
→
A group of hydrogen atoms are prepared in n = 4 states. List the wavelength that are emitted as the atoms make transitions and return to n = 2 states.
→
The descending pulley shown in figure has a radius 20cm and moment of inertia 0.20kg-m2. The fixed pulley is light and the horizontal plane frictionless. Find the acceleration of the block if its mass is 1.0kg.

→
  1. Draw the circuit arrangement for studying the input and output characteristics of an n-p-n transistor in CE configuration. With the help of these characteristics define (i) input resistance, (ii) current amplification factor.
  2. Describe briefly with the help of a circuit diagram how an n-p-n transistor is used to produce self-sustained oscillations.
→