Question 303: Waves Optics

Question

A single slit of width $d$ is illuminated by violet light of wavelength 400 nm and the width of the diffraction pattern is measured as ' Y '. When half of the slit width is covered and illuminated by yellow light of wavelength 600 nm , the width of the diffraction pattern is

Accepted Answer

To find the width of the diffraction pattern when the slit is partially covered, we start with the formula for the width of the diffraction pattern:
$ \mathrm{W} = \frac{2 \lambda \mathrm{D}}{\mathrm{d}} \quad	ext{(i)} $
Given:
The initial wavelength, $ \lambda = 400 \, 	ext{nm} $
The initial slit width, $ \mathrm{d} $
The initial width of the diffraction pattern is $ \mathrm{Y} $
Now, when half of the slit is covered, the effective width of the slit becomes:
$ \mathrm{d}^{\prime} = \frac{\mathrm{d}}{2} $
The new wavelength is $ \lambda^{\prime} = 600 \, 	ext{nm} $.
Substituting these values into our formula, the new width of the diffraction pattern is:
$  \begin{align*} \mathrm{W}^{\prime} &= \frac{2 \lambda^{\prime} \mathrm{D}}{\mathrm{d}^{\prime}} \ &= \frac{2 \cdot 600 \, 	ext{nm} \cdot \mathrm{D}}{\mathrm{d} / 2} \quad 	ext{(ii)} \end{align*}  $
So, comparing the new width to the original:
$ \begin{align*} \frac{\mathrm{W}^{\prime}}{\mathrm{W}} &= \frac{2 \lambda^{\prime} \mathrm{D}}{\lambda \mathrm{D}} \ &= \frac{2 	imes 600}{400} \ &= 3 \end{align*} $
Thus, the new width of the diffraction pattern, $\mathrm{W}^{\prime}$, is:
$ \mathrm{W}^{\prime} = 3 \mathrm{W} = 3 \mathrm{Y} $
Therefore, the width of the diffraction pattern, when half the slit is covered and illuminated by yellow light, becomes three times the initial width, or $3Y$.

Answer

zero

Answer

$\frac{Y}{3}$

Answer

3 Y

Answer

4 Y

Waves Optics

A single slit of width d is illuminated by violet light of wavelength 400 nm and the width of the diffraction pattern is measured as ' Y '. When half of the slit width is covered and illuminated by yellow light of wavelength 600 nm , the width of the diffraction pattern is

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