Wave Optics

Step 1: Use the formula for fringe width in Young's double slit experiment.
The fringe width ( $%5Cbeta$ ) in Young's double slit experiment is given by:
$%5Cbeta%20%3D%20%5Cfrac%7B%5Clambda%20D%7D%7Bd%7D$ where: $%5Clambda$ is the wavelength of light, $D$ is the distance of the screen from the slits, $d$ is the slit separation.
Step 2: Plug in the given values.

We are given:
$%5Clambda%20%3D%20620%20%5C%2C%20%5Ctext%7Bnm%7D%20%3D%20620%20%5Ctimes%2010%5E%7B-9%7D%20%5C%2C%20%5Ctext%7Bm%7D$ , $d%20%3D%200.3%20%5C%2C%20%5Ctext%7Bmm%7D%20%3D%200.3%20%5Ctimes%2010%5E%7B-3%7D%20%5C%2C%20%5Ctext%7Bm%7D$ , $%5Cbeta%20%3D%201.3%20%5C%2C%20%5Ctext%7Bmm%7D%20%3D%201.3%20%5Ctimes%2010%5E%7B-3%7D%20%5C%2C%20%5Ctext%7Bm%7D$ . Rearrange the formula to find $D$ : $D%20%3D%20%5Cfrac%7B%5Cbeta%20d%7D%7B%5Clambda%7D$ Substitute the values: $D%20%3D%20%5Cfrac%7B(1.3%20%5Ctimes%2010%5E%7B-3%7D)%20%5Ctimes%20(0.3%20%5Ctimes%2010%5E%7B-3%7D)%7D%7B620%20%5Ctimes%2010%5E%7B-9%7D%7D%20%5C%2C%20%5Ctext%7Bm%7D$ $D%20%3D%206.29%20%5C%2C%20%5Ctext%7Bm%7D$
Step 3: Conclusion.
Thus, the distance of the screen from the source is 6.29 m.
Conclusion:
The correct answer is (B) 6.29 m.

Step 1: Use the formula for the number of images produced by two mirrors.
The number of images

n

produced by two plane mirrors is
given by the formula:

n%20%3D%20%5Cfrac%7B360%5E%5Ccirc%7D%7B%5Ctheta%7D%20-%201

where

%5Ctheta

is the angle between the mirrors.
Step 2: Apply the initial condition.
Initially, 5 images are produced, so:

%5Cfrac%7B360%5E%5Ccirc%7D%7B%5Ctheta%7D%20-%201%20%3D%205

%5Cfrac%7B360%5E%5Ccirc%7D%7B%5Ctheta%7D%20%3D%206%20%5Cquad%20%5CRightarrow%20%5Cquad%20%5Ctheta%20%3D%2060%5E%5Ccirc

Step 3: Change the angle.
Now, the angle is decreased by 30°, so the new angle is:

%5Ctheta'%20%3D%2060%5E%5Ccirc%20-%2030%5E%5Ccirc%20%3D%2030%5E%5Ccirc

Step 4: Calculate the new number of images.
Using the formula for the new angle:

n'%20%3D%20%5Cfrac%7B360%5E%5Ccirc%7D%7B30%5E%5Ccirc%7D%20-%201%20%3D%2012%20-%201%20%3D%2011

Step 5: Conclusion.
Thus, the number of images will be 11.
Conclusion:
The correct answer is (C) 11.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Wave Optics

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs