Given below are two statements, one labeled as Assertion (A) and the other as Reason (R).
Assertion (A): In Young’s double slit experiment, the fringes produced by red light are closer compared to those produced by blue light.
Reason (R): The fringe width is directly proportional to the wavelength of light.
In the light of the above statements, choose the correct answer from the options given below:
Show Hint
In Young’s double-slit experiment:
- Fringe width is given by \( \beta = \frac{\lambda D}{d} \).
- Longer wavelengths (e.g., red) produce wider fringes.
- Shorter wavelengths (e.g., blue) produce narrower fringes.
Both (A) and (R) are true, but (R) is NOT the correct explanation of (A).
(A) is false, but (R) is true.
Both (A) and (R) are true, and (R) is the correct explanation of (A).
(A) is true, but (R) is false.
Show Solution
The Correct Option isB
Solution and Explanation
Step 1: Fringe Width Formula.The fringe width (\(\beta\)) in Young's double-slit experiment is defined by the equation:\[\beta = \frac{\lambda D}{d},\]with the following variables:- \( \lambda \): Wavelength of light.- \( D \): Distance from slits to the screen.- \( d \): Separation between the slits.Step 2: Evaluation of Assertion (A).As fringe width is directly proportional to wavelength (\( \beta \propto \lambda \)), red light (longer \( \lambda \)) will generate wider fringes than blue light (shorter \( \lambda \)).Assertion (A) is consequently false as it asserts the reverse.Step 3: Evaluation of Reason (R).The statement that fringe width is proportional to wavelength is accurate.Given that Assertion (A) is false and Reason (R) is true, the correct selection is:\[\boxed{\text{(2) (A) is false, but (R) is true.}}\]
