NEET Wave Optics — Set 22

Question 1

What is the path difference for the fourth bright fringe in a double-slit experiment?

Accepted Answer

Constructive interference occurs at $ \Delta = n\lambda $. For the fourth bright fringe, $ n = 4 $, so $ \Delta = 4\lambda $.

Question 2

What is the resultant amplitude of two coherent waves of amplitude $ a $ with a phase difference of $ 4\pi $?

Accepted Answer

Resultant amplitude $ A = 2a \cos(\phi/2) $. For $ \phi = 4\pi $, $ A = 2a \cos(2\pi) = 2a \times 1 = 2a $.

Question 3

What is the intensity at a point in a double-slit experiment where the path difference is $ \lambda/3 $, if the maximum intensity is $ 4I_0 $?

Accepted Answer

Intensity $ I = 4I_0 \cos^2(\phi/2) $, where $ \phi = \frac{2\pi}{\lambda} \Delta $. For $ \Delta = \frac{\lambda}{3} $, $ \phi = \frac{2\pi}{\lambda} \cdot \frac{\lambda}{3} = \frac{2\pi}{3} $, $ I = 4I_0 \cos^2\left(\frac{\pi}{3}\right) = 4I_0 \left(\frac{1}{2}\right)^2 = 4I_0 \times \frac{1}{4} = I_0 $.

NEET Physics: Wave Optics — Practice Set 22

Q1. What is the path difference for the fourth bright fringe in a double-slit experiment?

Q2. What is the resultant amplitude of two coherent waves of amplitude \( a \) with a phase difference of \( 4\pi \)?

Q3. What is the intensity at a point in a double-slit experiment where the path difference is \( \lambda/3 \), if the maximum intensity is \( 4I_0 \)?

Q4. What causes the intensity to vary when a second polaroid is rotated in front of another polaroid through which unpolarized light has passed?

Q5. What is the condition for coherence in a double-slit experiment?

Q6. Why does the wave nature of light allow it to produce a pattern of bright and dark regions when passing through a narrow slit?

Q7. What is the angular position of the first minimum in a single-slit diffraction pattern if the slit width is \( 15.0 \, \mu\text{m} \) and the wavelength is \( 750 \, \text{nm} \)?

Q8. What is the path difference for the sixth dark fringe in a double-slit experiment?

Q9. What causes the intensity of light to vary sinusoidally with angle when passing through two polaroids?

Q10. What is the phase difference for destructive interference in a double-slit experiment when the path difference is \( \lambda \)?