Question 365: Wave Optics

Question

A single slit diffraction pattern is formed with white light. For what wavelength of light the $3^{	ext {rd }}$ secondary maximum in diffraction pattern coincides with the $2^{	ext {nd }}$ secondary maximum in the pattern of red light of wavelength 6000 $\mathop A\limits^o $ ?

Accepted Answer

$\begin{aligned} & 	ext { Distance of nth maximum } \mathrm{y}_{\mathrm{n}}=\left(\mathrm{n}+\frac{1}{2}ight) \frac{\lambda \mathrm{D}}{\mathrm{a}} \ & 	herefore \quad \mathrm{y}_2=\left(2+\frac{1}{2}ight) \frac{\lambda_1 \mathrm{D}}{\mathrm{a}} 	ext { and } \mathrm{y}_3=\left(3+\frac{1}{2}ight) \frac{\lambda_2 \mathrm{D}}{\mathrm{a}} \ & 	herefore \quad 2.5 \lambda_1=3.5 \lambda_2 \ & 	herefore \quad 2.5 	imes 6000=3.5 \lambda_2 \ & 	herefore \quad \lambda_2=\frac{2.5 	imes 6000}{3.5} \approx 4300 \mathop A\limits^o\end{aligned}$

Answer

4500 $\mathop A\limits^o $

Answer

3500 $\mathop A\limits^o $

Answer

4000 $\mathop A\limits^o $

Answer

5000 $\mathop A\limits^o $

Wave Optics

A single slit diffraction pattern is formed with white light. For what wavelength of light the 3^{\text{rd }} secondary maximum in diffraction pattern coincides with the 2^{\text{nd }} secondary maximum in the pattern of red light of wavelength 6000 \mathop A\limits^o ?

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