NEET Wave Optics — Set 20

Question 1

What is the intensity of light after passing through two polaroids with pass-axes at $ 45^\circ $, if the initial unpolarized intensity is $ I_0 $?

Accepted Answer

After the first polaroid, $ I = \frac{I_0}{2} $. After the second at $ 45^\circ $, $ I = \frac{I_0}{2} \cos^2 45^\circ = \frac{I_0}{2} \times \frac{1}{2} = \frac{I_0}{4} $.

Question 2

In a double-slit experiment, if two wavelengths $ 600 \, \text{nm} $ and $ 400 \, \text{nm} $ are used, what is the smallest distance from the central maximum where their bright fringes coincide? ($ d = 0.2 \, \text{mm} $, $ D = 1.0 \, \text{m} $)

Accepted Answer

Bright fringe position $ x_n = \frac{n \lambda D}{d} $. Fringes coincide when $ n_1 \lambda_1 = n_2 \lambda_2 $. $ 600 n_1 = 400 n_2 $, $ n_2 = \frac{3}{2} n_1 $. Smallest integers: $ n_1 = 2 $, $ n_2 = 3 $. $ x = \frac{2 \times 6.0 \times 10^{-7} \times 1.0}{2.0 \times 10^{-4}} = 6.0 \times 10^{-3} \, \text{m} = 6.0 \, \text{mm} $.

Question 3

Why does the interference pattern from two slits disappear if the slits are too far apart?

Accepted Answer

Large slit separation reduces the overlap of wavefronts, disrupting the consistent path difference needed for stable interference.

NEET Physics: Wave Optics — Practice Set 20

Q1. What is the intensity of light after passing through two polaroids with pass-axes at \( 45^\circ \), if the initial unpolarized intensity is \( I_0 \)?

Q2. In a double-slit experiment, if two wavelengths \( 600 \, \text{nm} \) and \( 400 \, \text{nm} \) are used, what is the smallest distance from the central maximum where their bright fringes coincide? (\( d = 0.2 \, \text{mm} \), \( D = 1.0 \, \text{m} \))

Q3. Why does the interference pattern from two slits disappear if the slits are too far apart?

Q4. What is the speed of light in a medium if its refractive index is 1.2 and the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

Q5. What is the shape of the refracted wavefront when a plane wave passes through a convex lens and converges to a point?

Q6. What is the path difference for the fifth dark fringe in a double-slit experiment?

Q7. What does the wave theory predict about the speed of light when it bends towards the normal during refraction?

Q8. What allows light to propagate through a vacuum without requiring a traditional medium?

Q9. What is the distance of the fourth bright fringe from the central maximum in a double-slit experiment if \( \lambda = 560 \, \text{nm} \), \( d = 0.35 \, \text{mm} \), and \( D = 1.4 \, \text{m} \)?

Q10. What is the angle of refraction when light is incident at the critical angle from a denser medium to a rarer medium?