Physics Q46 – JEE-MAIN 2025

In a Young's double slit experiment, two slits are located

1.5 mm

apart. The distance of screen from slits is

2 m

and the wavelength of the source is

400 nm

. If the

20

maxima of the double slit pattern are contained within the central maximum of the single slit diffraction pattern, then the width of each slit is

x \times 10^{- 3} cm

, where

x

-value is _______.

Enter Calculated Numerical Value:

Clue 1 of 3: Understanding the condition

The problem describes a scenario where the double-slit interference pattern is modulated by a single-slit diffraction envelope.

🧠 Full Solution Path

Step 1: Identify Given Parameters and Condition✦ Active

Given parameters are: slit separation $d = 1.5 mm = 1.5 \times 10^{- 3} m$ , screen distance $D = 2 m$ , and wavelength $λ = 400 nm = 400 \times 10^{- 9} m = 4 \times 10^{- 7} m$ . The condition states that 20 double-slit maxima are within the central single-slit maximum. This implies that the $10^{t h}$ double-slit maximum (on either side of the central maximum) coincides with the first minimum of the single-slit diffraction pattern.

Step 2: Apply Formulas for Maxima and Minima○ Expand

The position of the $n^{t h}$ maximum in a double-slit experiment is given by $y_{n, d s} = \frac{n λ D}{d}$ . For the $10^{t h}$ maximum, $y_{10, d s} = \frac{10 λ D}{d}$ . The position of the first minimum in a single-slit diffraction pattern is given by $y_{1, s s} = \frac{λ D}{a}$ , where $a$ is the width of each slit.

\frac{10 λ D}{d} = \frac{λ D}{a}

💡 Teacher's Secret Hint

Ensure correct 'n' value for the double-slit maximum that coincides with the first single-slit minimum.

Step 3: Solve for Slit Width and Convert Units○ Expand

Cancel out $λ D$ from both sides of the equation:

\frac{10}{d} = \frac{1}{a} ⟹ a = \frac{d}{10}

Substitute the value of $d$ :

a = \frac{1.5 \times 10^{- 3} m}{10} = 0.15 \times 10^{- 3} m = 1.5 \times 10^{- 4} m

Convert the slit width $a$ from meters to centimeters and express it in the form $x \times 10^{- 3} cm$ :

a = 1.5 \times 10^{- 4} m \times (\frac{100 cm}{1 m}) = 1.5 \times 10^{- 2} cm = 15 \times 10^{- 3} cm

Comparing this with $x \times 10^{- 3} cm$ , we find $x = 15$ .

💡 Teacher's Secret Hint

Pay close attention to unit conversions, especially from meters to centimeters and expressing in the required scientific notation.

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Physics Question 46 – JEE-MAIN 2025

Clue 1 of 3: Understanding the condition

🧠 Full Solution Path