Physics Q46 – JEE-MAIN 2026

In a Young's double slit experiment, the intensity at some point on the screen is found to be

\frac{3}{4}

times of the maximum of the interference pattern. The path difference between the interfering waves at this point is

\frac{λ}{x}

where

λ

is wavelength of the incident light. The value of

x

is _______.

Enter Calculated Numerical Value:

Clue 1 of 3: Intensity in YDSE

Recall the formula for intensity in Young's double-slit experiment in terms of maximum intensity and phase difference.

🧠 Full Solution Path

Step 1: Relate Intensity to Phase Difference✦ Active

The intensity $I$ at any point in Young's double-slit experiment is given by $I = I_{m a x} \cos^{2} (\frac{ϕ}{2})$ , where $I_{m a x}$ is the maximum intensity and $ϕ$ is the phase difference. Given that $I = \frac{3}{4} I_{m a x}$ , we can write:

\frac{3}{4} I_{m a x} = I_{m a x} \cos^{2} (\frac{ϕ}{2})

This simplifies to:

\cos^{2} (\frac{ϕ}{2}) = \frac{3}{4}

Step 2: Calculate Phase Difference○ Expand

Taking the square root of both sides, we get:

\cos (\frac{ϕ}{2}) = \pm \frac{\sqrt{3}}{2}

For the smallest non-zero path difference, we consider the positive value. Thus, $\frac{ϕ}{2} = \frac{π}{6}$ (or $30^{\circ}$ ). Therefore, the phase difference is:

ϕ = \frac{2 π}{6} = \frac{π}{3}

💡 Teacher's Secret Hint

Remember that $\cos (θ) = \frac{\sqrt{3}}{2}$ for $θ = \frac{π}{6}$ .

Step 3: Determine Path Difference and x○ Expand

The phase difference $ϕ$ is related to the path difference $Δ x$ by the formula $ϕ = \frac{2 π}{λ} Δ x$ . Substituting the calculated phase difference:

\frac{π}{3} = \frac{2 π}{λ} Δ x

Solving for $Δ x$ :

Δ x = \frac{λ}{3} \cdot \frac{1}{2} = \frac{λ}{6}

The problem states that the path difference is $\frac{λ}{x}$ . Comparing this with our result:

\frac{λ}{x} = \frac{λ}{6}

Thus, the value of $x$ is:

x = 6

💡 Teacher's Secret Hint

Ensure units are consistent when relating phase and path difference.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 46 – JEE-MAIN 2026

Clue 1 of 3: Intensity in YDSE

🧠 Full Solution Path