Unit 14: Waves , Sound , and Physical Optics
Weightage : 15–18%
The fact that two oncoming headlights of a car cannot be resolved at large distances (i.e., the two light sources are seen as one) is best described by
Correct Answer: \( \boxed{\mathrm{D}} \)
Light behaves as a wave and undergoes diffraction as it passes through an aperture or around an obstacle. Each headlight produces a diffraction pattern that spreads as it travels.
At very large distances, the diffraction patterns from the two headlights overlap, making the two sources appear as a single light source. This phenomenon limits the ability of an optical system, including the human eye, to distinguish two nearby objects.
The minimum angular separation that can be resolved is described by the Rayleigh criterion:
\( \theta_{\mathrm{min}} \approx 1.22\frac{\lambda}{D} \)
where \( \lambda \) is the wavelength of light and \( D \) is the diameter of the aperture (such as the pupil of the eye or a telescope).
Therefore, the inability to distinguish two distant headlights is best explained by diffraction.
Therefore, the correct answer is (D).
A shadow is formed by a point source of light. Upon closer inspection, the edges of the shadow seem to be diffuse and fuzzy. This phenomenon is probably caused by
Correct Answer: \( \boxed{\mathrm{C}} \)
Diffraction is the bending and spreading of waves around the edges of obstacles or through narrow openings. According to Huygens’ principle, every point on a wavefront acts as a source of secondary wavelets.
At the edges of the shadow-forming object, light waves bend slightly into the geometric shadow region. As a result, the transition from bright to dark is gradual rather than perfectly sharp, producing diffuse or fuzzy shadow edges.
Dispersion separates different wavelengths but does not produce fuzzy shadow boundaries, and refraction requires light to pass between different media, which is not occurring here.
Therefore, the correct answer is (C).
In an experiment, monochromatic light of frequency \(f_{1}\) and wavelength \( \lambda_{1} \) passes through a single slit of width \(d_{1}\) to produce light and dark bands on a screen as seen in pattern 1. The screen is a distance \(L_{1}\) from the slit. A single change to the experimental setup is made and pattern 2 is created on the screen. Which of the following would account for the differences seen in the patterns?
Correct Answer: \( \boxed{\mathrm{A}} \)
Pattern 2 has more closely spaced bright and dark fringes than Pattern 1, indicating that the diffraction angle has decreased.
For single-slit diffraction, the minima satisfy
\( d\sin\theta=m\lambda \)
or
\( \sin\theta=\dfrac{m\lambda}{d} \)
To produce a smaller diffraction angle and therefore a tighter fringe spacing, the wavelength must decrease or the slit width must increase.
Since the wavelength and slit width changes given in choices (B) and (D) would both increase the diffraction angle, they cannot produce Pattern 2. Increasing the screen distance, as in (C), would spread the pattern farther apart rather than closer together.
Because the speed of light is constant in air,
\( c=f\lambda \)
Increasing the frequency decreases the wavelength. Thus, if \(f_{1}<f_{2}\), then \(\lambda_{2}<\lambda_{1}\), resulting in a narrower diffraction pattern with smaller fringe spacing.
Therefore, the correct answer is (A).
