Interference Of Light Waves And Young S Experiment

Step 1: Concept
Slit width ratio

w_%7B1%7D%2Fw_%7B2%7D

is equal to the intensity ratio

I_%7B1%7D%2FI_%7B2%7D

, and intensity

I%20%5Cpropto%20A%5E%7B2%7D

.
Step 2: Analysis

I_%7B1%7D%2FI_%7B2%7D%20%3D%201%2F4%20%5CRightarrow%20(A_%7B1%7D%2FA_%7B2%7D)%5E%7B2%7D%20%3D%201%2F4%20%5CRightarrow%20A_%7B2%7D%20%3D%202A_%7B1%7D

.
Step 3: Calculation

%5Cfrac%7BI_%7Bmax%7D%7D%7BI_%7Bmin%7D%7D%20%3D%20%5Cfrac%7B(A_%7B1%7D%20%2B%20A_%7B2%7D)%5E%7B2%7D%7D%7B(A_%7B1%7D%20-%20A_%7B2%7D)%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B(A_%7B1%7D%20%2B%202A_%7B1%7D)%5E%7B2%7D%7D%7B(A_%7B1%7D%20-%202A_%7B1%7D)%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B(3A_%7B1%7D)%5E%7B2%7D%7D%7B(-A_%7B1%7D)%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B9%7D%7B1%7D

.
Step 4: Conclusion
Hence, the ratio is 9:1.
Final Answer:(C)

Step 1: Understanding the Concept:
This problem requires the direct application of the formula for fringe width in a Young's double-slit experiment (YDSE). The fringe width is the separation between consecutive bright fringes or consecutive dark fringes.

Step 2: Key Formula or Approach:
The fringe width ( $%5Cbeta$ ) in a YDSE is given by the formula: $%5Cbeta%20%3D%20%5Cfrac%7B%5Clambda%20D%7D%7Bd%7D$ where $%5Clambda$ is the wavelength of the light, $D$ is the distance from the slits to the screen, and $d$ is the distance between the two slits.

Step 3: Detailed Explanation:
Given data:
Slit separation, $d%20%3D%201.5%20%5C%2C%20%5Ctext%7Bmm%7D%20%3D%201.5%20%5Ctimes%2010%5E%7B-3%7D%20%5C%2C%20%5Ctext%7Bm%7D$ .
Screen distance, $D%20%3D%201.2%20%5C%2C%20%5Ctext%7Bm%7D$ .
Wavelength, $%5Clambda%20%3D%20600%20%5C%2C%20%5Ctext%7Bnm%7D%20%3D%20600%20%5Ctimes%2010%5E%7B-9%7D%20%5C%2C%20%5Ctext%7Bm%7D%20%3D%206%20%5Ctimes%2010%5E%7B-7%7D%20%5C%2C%20%5Ctext%7Bm%7D$ .
Calculation:
It is essential to use consistent units (SI units are recommended). Substitute the values into the formula: $%5Cbeta%20%3D%20%5Cfrac%7B(6%20%5Ctimes%2010%5E%7B-7%7D%20%5C%2C%20%5Ctext%7Bm%7D)%20%5Ctimes%20(1.2%20%5C%2C%20%5Ctext%7Bm%7D)%7D%7B1.5%20%5Ctimes%2010%5E%7B-3%7D%20%5C%2C%20%5Ctext%7Bm%7D%7D$ $%5Cbeta%20%3D%20%5Cfrac%7B7.2%20%5Ctimes%2010%5E%7B-7%7D%7D%7B1.5%20%5Ctimes%2010%5E%7B-3%7D%7D%20%5C%2C%20%5Ctext%7Bm%7D$ $%5Cbeta%20%3D%204.8%20%5Ctimes%2010%5E%7B-4%7D%20%5C%2C%20%5Ctext%7Bm%7D$ The options are in millimeters (mm). To convert from meters to millimeters, multiply by $10%5E3$ . $%5Cbeta%20%3D%20(4.8%20%5Ctimes%2010%5E%7B-4%7D)%20%5Ctimes%2010%5E3%20%5C%2C%20%5Ctext%7Bmm%7D%20%3D%204.8%20%5Ctimes%2010%5E%7B-1%7D%20%5C%2C%20%5Ctext%7Bmm%7D%20%3D%200.48%20%5C%2C%20%5Ctext%7Bmm%7D$

Step 4: Final Answer:
The fringe width will be 0.48 mm.

Interference Of Light Waves And Young S Experiment

High-Yield Trend

Chapter Questions
3 MCQs

Official Solution

Official Solution

Official Solution

Interference Of Light Waves And Young S Experiment

High-Yield Trend

Chapter Questions 3 MCQs

Official Solution

Official Solution

Official Solution

Chapter Questions
3 MCQs