Question 235: Wave Optics

Question

A single slit diffraction pattern is formed with white light. For what wavelength of light the $4^{	ext {th }}$ secondary maximum in diffraction pattern coincides with the $3^{	ext {rd }}$ secondary maximum in the pattern of light of wavelength ' $\lambda$ '?

Accepted Answer

Position of $n^{	ext {th }}$ secondary maximum in a singleslit diffraction pattern is given by
$$ y_{\mathrm{s}}=(2 \mathrm{n}+1) \frac{\lambda \mathrm{D}}{2 \mathrm{a}} $$
For $4^{	ext {th }}$ secondary maximum,
$$ y_4=\frac{9 \lambda^{\prime} \mathbf{D}}{2 a} $$
For $3^{	ext {rd }}$ secondary maximum,
$$ y_3==\frac{7 \lambda D}{2 a} $$
$4^{	ext {th }}$ and $3^{	ext {rd }}$ secondary maximum coincides,
$$ \begin{aligned} & 	herefore \quad y_4=y_3 \ & \frac{9 \lambda^{\prime} D}{2 a}=\frac{7 \lambda D}{2 a} \ & \lambda^{\prime}=\frac{7 \lambda}{9} \end{aligned} $$

Answer

$\frac{5 \lambda}{7}$

Answer

$\frac{7 \lambda}{9}$

Answer

$\frac{3 \lambda}{4}$

Answer

$\frac{9 \lambda}{13}$

Wave Optics

A single slit diffraction pattern is formed with white light. For what wavelength of light the 4^{\text {th }} secondary maximum in diffraction pattern coincides with the 3^{\text {rd }} secondary maximum in the pattern of light of wavelength ' \lambda '?

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