CBSE 2024, Set 1

Question

A beam of light consisting of a known wavelength $520	ext{ nm}$ and an unknown wavelength $\lambda$, used in Young's double slit experiment produces two interference patterns such that the fourth bright fringe of unknown wavelength coincides with the fifth bright fringe of known wavelength. Find the value of $\lambda$.

Edvaya · Accepted Answer

The correct answer is Subjective. **SOLUTION** The position of the $n^{	ext{th}}$ bright fringe from the central maximum in Young's Double Slit Experiment (YDSE) is given by: $$y_n = \frac{n \lambda D}{d}$$ We are given that the $4^{	ext{th}}$ bright fringe of the unknown wavelength ($\lambda_2 = \lambda$) perfectly coincides with the $5^{	ext{th}}$ bright fringe of the known wavelength ($\lambda_1 = 520	ext{ nm}$). $$y_4 (	ext{of } \lambda_2) = y_5 (	ext{of } \lambda_1)$$ $$\frac{4 \lambda_2 D}{d} = \frac{5 \lambda_1 D}{d}$$ Since $D$ (screen distance) and $d$ (slit separation) are strictly constant for the experimental setup, they cancel out: $$4 \lambda_2 = 5 \lambda_1$$ $$4 \lambda = 5 	imes 520	ext{ nm}$$ $$\lambda = \frac{2600}{4}$$ $$\lambda = 650	ext{ nm}$$ The unknown wavelength $\lambda$ is **$650	ext{ nm}$**.

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Physics > Optics > Wave Optics

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