Given Data Wavelength of light, λ=6000Å=6000×10−10m Refractive index of glass plate, n=1.5 Angle of refraction, r=60∘ Formula for Destructive Interference The condition for destructive interference (dark fringe) in the reflected light for the smallest thickness is: 2nt‌cos‌r=λ
Applying the Given Values Substitute the given values into the formula: 2×1.5×t×cos‌60∘=6000×10−10m Since cos‌60∘=0.5, the equation simplifies to: ‌2×1.5×t×0.5=6000×10−10m ‌1.5×t=6000×10−10m t=‌
6000×10−10m
1.5
Solving for t : ‌t=4000×10−10m ‌t=4×10−7m Correct Answer Option D: 4×10−7m