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
- 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.
The Correct Option is B
Approach Solution - 1
Approach Solution -2
Step 1: Formula for fringe width in Young’s double slit experiment.
The fringe width is given by: \[ \beta = \frac{\lambda D}{d} \] where \( \lambda \) = wavelength of light, \( D \) = distance between slits and screen, \( d \) = distance between the two slits.
Step 2: Relation between fringe width and wavelength.
From the above formula: \[ \beta \propto \lambda \] i.e., the fringe width is directly proportional to the wavelength.
Step 3: Compare red and blue light.
The wavelength of red light (\( \lambda_r \)) is greater than that of blue light (\( \lambda_b \)): \[ \lambda_r > \lambda_b. \] Hence, the fringes produced by red light are wider apart (not closer) than those produced by blue light.
Step 4: Verify the truth of the statements.
- Assertion (A): False — because red fringes are farther apart, not closer. - Reason (R): True — because fringe width is directly proportional to wavelength.
Final Answer:
\[ \boxed{(A)\ \text{is false, but (R) is true.}} \]
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