JEE Main 2025 · 22 January · morning · Single correct · +4 / −1
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.
Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements, choose the most appropriate answer from the options given below :
- (a) (A) is false but (R) is true
- (b) Both (A) and (R) are true but (R) is not the correct explanation of (A)
- (c) Both (A) and (R) are true and (R) is the correct explanation of (A)
- (d) (A) is true but (R) is false
Answer and solution
Answer (c) Both (A) and (R) are true and (R) is the correct explanation of (A)
Solution
Physics sir · 4 steps
In a denser medium the wavelength shrinks, and fringe width shrinks right along with it.
- Check the Reason. Frequency is set by the source, so it stays the same when light enters a new medium. The speed drops to v = c/μ, where μ > 1 is the refractive index. So (R) is true.
- Wavelength in medium. Since v = fλ and f is fixed, the wavelength falls in the same ratio as the speed: λ' = λ/μ.
β' = (λ' D)/d = (λ D)/(μ d) = β/μ
- Check the Assertion. With μ > 1, the fringe width β' is smaller than β in air, so consecutive fringes do come closer. (A) is true.
- So. The fringes come closer because the wavelength shrinks, and the wavelength shrinks because the speed drops while the frequency stays fixed. That is exactly what (R) states, so (R) correctly explains (A). The answer is (c).
The idea to keep. When light enters a medium, frequency stays fixed and wavelength becomes λ/μ. Anything that depends on λ, like fringe width β = λ D/d, scales down by μ too.
Answer from the NTA final answer key. Solution by PrepWiser.