A thin glass plate of thickness 2500/3λ ( λ is wavelength of light… | JEE Main 2013 (25 Apr, Shift 1)

Q67JEE Main 2013 · 25 APR · SHIFT 1Medium

YDSE: Film, Medium & Two Wavelengths

A thin glass plate of thickness $\frac{2500}{3}\lambda$ ( $\lambda$ is wavelength of light used) and refractive index $\mu = 1.5$ is inserted between one of the slits and the screen in Young's double slit experiment. At a point on the screen equidistant from the slits, the ratio of the intensities before and after the introduction of the glass plate is:

Show answer and solution

Answer: (c)

Before: path difference $0$ , so $I = 4I_0$ (max).
After: $\Delta = (\mu - 1)t = 0.5 \times \frac{2500}{3}\lambda = 416\tfrac{2}{3}\lambda$ , so phase $\phi = 2\pi \times \tfrac{2}{3} = \tfrac{4\pi}{3}$ (mod $2\pi$ ).
$I' = 4I_0\cos^2(\phi/2) = 4I_0\cos^2\tfrac{2\pi}{3} = I_0$
Ratio $4I_0 : I_0 = 4:1$ . So the answer is (c) 4 : 1.

Report a mistake

YDSE: Film, Medium & Two Wavelengths question from JEE Main 2013 (25 Apr, Shift 1)

More questions on YDSE: Film, Medium & Two Wavelengths