Physics Q33 – JEE-MAIN 2026

Home Physics Units & MeasurementsQuestion #552

A slit of width

a

is illuminated by light of wavelength

λ

. The linear separation between

1^{st}

and

3^{rd}

minima in the diffraction pattern produced on a screen placed at a distance

D

from the slit system is _______.

Clue 1 of 3: Single-Slit Diffraction Minima

Recall the condition for destructive interference (minima) in a single-slit diffraction pattern.

🧠 Full Solution Path

Step 1: Identify the condition for minima in single-slit diffraction✦ Active

For a single slit of width $a$ , the condition for the $m$ -th minimum (destructive interference) is given by:

a \sin θ_{m} = m λ

where $θ_{m}$ is the angular position of the $m$ -th minimum, $λ$ is the wavelength of light, and $m = \pm 1, \pm 2, \dots$ (excluding $m = 0$ for minima).

Step 2: Determine the linear position of the minima on the screen○ Expand

For small angles, which is typical for diffraction patterns observed on a screen far from the slit, we can use the approximation $\sin θ_{m} \approx \tan θ_{m} = \frac{y_{m}}{D}$ , where $y_{m}$ is the linear distance from the central maximum to the $m$ -th minimum on the screen, and $D$ is the distance from the slit to the screen.

Substituting this into the condition from Step 1:

a \frac{y_{m}}{D} = m λ

Solving for $y_{m}$ , we get the linear position of the $m$ -th minimum:

y_{m} = \frac{m λ D}{a}

💡 Teacher's Secret Hint

Remember that the small angle approximation is crucial here. If angles are not small, the problem becomes more complex.

Step 3: Calculate the linear separation between the

1^{st}

and

3^{rd}

minima○ Expand

For the $1^{st}$ minimum ( $m = 1$ ):

y_{1} = \frac{1 \cdot λ D}{a} = \frac{λ D}{a}

For the $3^{rd}$ minimum ( $m = 3$ ):

y_{3} = \frac{3 \cdot λ D}{a} = \frac{3 λ D}{a}

The linear separation between the $1^{st}$ and $3^{rd}$ minima is the absolute difference of their positions:

Δ y = | y_{3} - y_{1} | = | \frac{3 λ D}{a} - \frac{λ D}{a} | = | \frac{(3 - 1) λ D}{a} | = \frac{2 λ D}{a}

💡 Teacher's Secret Hint

Ensure you correctly identify the 'm' values for the specified minima. The central maximum is at $m = 0$ , and minima are indexed starting from $m = 1$ outwards.

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Physics Question 33 – JEE-MAIN 2026

Clue 1 of 3: Single-Slit Diffraction Minima

🧠 Full Solution Path