NEET Wave Optics — Set 18

Question 1

What is the angular position of the first secondary maximum in a single-slit diffraction pattern if the slit width is $ 6.0 \, \mu\text{m} $ and the wavelength is $ 600 \, \text{nm} $?

Accepted Answer

First secondary maximum occurs at $ \theta \approx \frac{3\lambda}{2a} $. $ \lambda = 6.0 \times 10^{-7} \, \text{m} $, $ a = 6.0 \times 10^{-6} \, \text{m} $. $ \sin \theta = \frac{3 \times 6.0 \times 10^{-7}}{2 \times 6.0 \times 10^{-6}} = 0.15 $, $ \theta = \sin^{-1}(0.15) \approx 8.6^\circ $.

Question 2

What is the fringe width in a double-slit experiment if $ \lambda = 660 \, \text{nm} $, $ d = 0.3 \, \text{mm} $, and $ D = 1.5 \, \text{m} $?

Accepted Answer

Fringe width $ \beta = \frac{\lambda D}{d} $. $ \lambda = 6.6 \times 10^{-7} \, \text{m} $, $ d = 3.0 \times 10^{-4} \, \text{m} $, $ D = 1.5 \, \text{m} $. $ \beta = \frac{6.6 \times 10^{-7} \times 1.5}{3.0 \times 10^{-4}} = 3.3 \times 10^{-3} \, \text{m} = 3.3 \, \text{mm} $.

Question 3

What is the distance of the first dark fringe from the central maximum in a double-slit experiment if $ \lambda = 650 \, \text{nm} $, $ d = 0.5 \, \text{mm} $, and $ D = 1.0 \, \text{m} $?

Accepted Answer

For the first dark fringe, $ x = \frac{\left(n + \frac{1}{2}\right) \lambda D}{d} $, $ n = 0 $. $ x = \frac{\frac{1}{2} \times 6.5 \times 10^{-7} \times 1.0}{5.0 \times 10^{-4}} = 6.5 \times 10^{-4} \, \text{m} = 0.65 \, \text{mm} $.

NEET Physics: Wave Optics — Practice Set 18

Q1. What is the angular position of the first secondary maximum in a single-slit diffraction pattern if the slit width is \( 6.0 \, \mu\text{m} \) and the wavelength is \( 600 \, \text{nm} \)?

Q2. What is the fringe width in a double-slit experiment if \( \lambda = 660 \, \text{nm} \), \( d = 0.3 \, \text{mm} \), and \( D = 1.5 \, \text{m} \)?

Q3. What is the distance of the first dark fringe from the central maximum in a double-slit experiment if \( \lambda = 650 \, \text{nm} \), \( d = 0.5 \, \text{mm} \), and \( D = 1.0 \, \text{m} \)?

Q4. In a single-slit diffraction pattern, what happens to the central maximum’s width if the wavelength is reduced to one-third?

Q5. What is the intensity of light in the photon picture, according to the wave optics concept?

Q6. What is the angular position of the second secondary maximum in a single-slit diffraction pattern if the slit width is \( 7.0 \, \mu\text{m} \) and the wavelength is \( 560 \, \text{nm} \)?

Q7. What is the distance of the first bright fringe from the central maximum in a double-slit experiment if \( \lambda = 620 \, \text{nm} \), \( d = 0.3 \, \text{mm} \), and \( D = 1.2 \, \text{m} \)?

Q8. What is the wavelength of light in a medium with refractive index 1.25 if its wavelength in air is \( 625 \, \text{nm} \)?

Q9. What is the resultant amplitude of two coherent waves of amplitude \( a \) with a phase difference of \( 7\pi/2 \)?

Q10. In a double-slit experiment, if \( \lambda = 460 \, \text{nm} \), \( d = 0.2 \, \text{mm} \), and \( D = 2.0 \, \text{m} \), what is the distance of the third bright fringe from the central maximum?