NEET Wave Optics — Set 11

Question 1

Why can’t two ordinary light sources, like sodium lamps, produce a stable interference pattern when illuminating two slits?

Accepted Answer

Ordinary sources emit light with rapidly changing phase differences, making them incoherent and unable to maintain a stable interference pattern.

Question 2

What is the angular width of the central maximum in a single-slit diffraction pattern if the slit width is $ 12.0 \, \mu\text{m} $ and the wavelength is $ 480 \, \text{nm} $?

Accepted Answer

Angular width $ 2\theta = \frac{2\lambda}{a} $. $ \lambda = 4.8 \times 10^{-7} \, \text{m} $, $ a = 1.2 \times 10^{-5} \, \text{m} $. $ \sin \theta = \frac{\lambda}{a} = \frac{4.8 \times 10^{-7}}{1.2 \times 10^{-5}} = 0.04 $, $ \theta = \sin^{-1}(0.04) \approx 2.3^\circ $, $ 2\theta \approx 4.6^\circ $.

Question 3

What is the speed of light in a medium with refractive index 1.45, 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 = 1.45 $, $ c = 3.0 \times 10^8 \, \text{m/s} $, $ v = \frac{3.0 \times 10^8}{1.45} \approx 2.07 \times 10^8 \, \text{m/s} $.

NEET Physics: Wave Optics — Practice Set 11

Q1. Why can’t two ordinary light sources, like sodium lamps, produce a stable interference pattern when illuminating two slits?

Q2. What is the angular width of the central maximum in a single-slit diffraction pattern if the slit width is \( 12.0 \, \mu\text{m} \) and the wavelength is \( 480 \, \text{nm} \)?

Q3. What is the speed of light in a medium with refractive index 1.45, given the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

Q4. In a diffraction experiment, if the slit width is \( 4.0 \, \mu\text{m} \) and the wavelength is \( 800 \, \text{nm} \), what is the angular position of the first minimum?

Q5. What explains the presence of alternate bright and dark bands near the edge of a shadow in diffraction?

Q6. What is the condition for the central maximum in a single-slit diffraction pattern?

Q7. What is the distance of the third dark fringe from the central maximum in a double-slit experiment if \( \lambda = 550 \, \text{nm} \), \( d = 0.25 \, \text{mm} \), and \( D = 2.0 \, \text{m} \)?

Q8. What causes the secondary maxima in a single-slit diffraction pattern to be weaker than the central maximum?

Q9. What is the fringe width in a double-slit experiment if \( \lambda = 620 \, \text{nm} \), \( d = 0.5 \, \text{mm} \), and \( D = 2.0 \, \text{m} \)?

Q10. What is the speed of light in a medium with a refractive index of 1.5, given the speed of light in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?