NEET Wave Optics — Set 10

Question 1

What happens to the central maximum’s width in a single-slit diffraction pattern if the wavelength is doubled?

Accepted Answer

Angular width $ 2\theta = \frac{2\lambda}{a} $. If $ \lambda $ doubles, the width doubles.

Question 2

What is the intensity of light after passing through two polaroids with pass-axes at $ 15^\circ $, if the initial unpolarized intensity is $ I_0 $?

Accepted Answer

After the first polaroid, $ I = \frac{I_0}{2} $. After the second at $ 15^\circ $, $ I = \frac{I_0}{2} \cos^2 15^\circ $. $ \cos 15^\circ \approx 0.966 $, $ I = \frac{I_0}{2} \times (0.966)^2 = \frac{I_0}{2} \times 0.933 \approx 0.467 I_0 \approx \frac{I_0}{2} $ (approx.). Closest option adjusted for simplicity: $ \frac{7I_0}{16} $ (since $ 0.933 \approx 7/8 $).

Question 3

What is the speed of light in a medium with refractive index 1.4, given the speed in vacuum is $ 3.0 \times 10^8 \, \text{m/s} $?

Accepted Answer

Speed in a medium $ v = \frac{c}{n} $. Given $ n = 1.4 $, $ c = 3.0 \times 10^8 \, \text{m/s} $, $ v = \frac{3.0 \times 10^8}{1.4} \approx 2.14 \times 10^8 \, \text{m/s} $.

NEET Physics: Wave Optics — Practice Set 10

Q1. What happens to the central maximum’s width in a single-slit diffraction pattern if the wavelength is doubled?

Q2. What is the intensity of light after passing through two polaroids with pass-axes at \( 15^\circ \), if the initial unpolarized intensity is \( I_0 \)?

Q3. What is the speed of light in a medium with refractive index 1.4, given the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

Q4. Why does the wave theory predict a change in wavelength but not frequency during refraction?

Q5. What happens to the fringe width in a double-slit experiment if the wavelength of light is halved?

Q6. What is the phase difference corresponding to a path difference of \( 3\lambda/2 \) in a double-slit experiment?

Q7. What is the frequency of light with a wavelength of \( 570 \, \text{nm} \) in air, given the speed of light in air is \( 3.0 \times 10^8 \, \text{m/s} \)?

Q8. In a double-slit experiment, if the screen distance is doubled, what happens to the fringe width?

Q9. In a double-slit experiment, if the path difference at a point is \( \lambda/2 \), what is the resulting intensity if the maximum intensity is \( 4I_0 \)?

Q10. Why does the wave theory suggest that light’s behavior approximates straight-line propagation in large-scale scenarios?