1. Use the condition for minima in single-slit diffraction

For a slit of width $a$, the minima are given by

$a\sin\theta = m\lambda, \qquad m=1,2,3,\dots$

For the first order minimum, $m=1$:

$a\sin\theta = \lambda$

Since the angle is small,

$\sin\theta \approx \tan\theta = \frac{y}{D}$

So,

$y = \frac{D\lambda}{a}$

where:

• $D = 100\text{ cm} = 1.0\text{ m}$
• $\lambda = 550\text{ nm} = 550\times 10^{-9}\text{ m}$
• $a = 0.20\text{ mm} = 0.20\times 10^{-3}\text{ m} = 2.0\times 10^{-4}\text{ m}$

2. Substitute the values

$y = \frac{(1.0)(550\times 10^{-9})}{2.0\times 10^{-4}}$

$y = \frac{550}{2.0}\times 10^{-5}$

$y = 275\times 10^{-5}\text{ m}$

3. Compare with the given form

Given distance is $x\times 10^{-5}\text{ m}$.

So,

$x=275$

4. Comparison with stored answer

Stored correct answer = $275$

This matches exactly.