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Chapter 16: Problem 2285

Wave light travels from an optically rarer medium to an optically denser medium its velocity decrease because of change in (A) frequency (B) wavelength (C) amplitude (D) phase

Short Answer

Expert verified
The correct answer is (B) wavelength. The wavelength of the light wave decreases when traveling from an optically rarer medium to an optically denser medium, causing the velocity to decrease as well.

Step by step solution

01

Recall Snell's Law and the Wave Equation

Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two media. \[n_1 \times \sin{\theta_1} = n_2 \times \sin{\theta_2}\] where \(n_1\) and \(n_2\) are the refractive indices of the rarer and denser media, and \(\theta_1\) and \(\theta_2\) are the angles of incidence and refraction. The wave equation relates the velocity (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) of a wave: \[v = f \lambda\]
02

Analyze the effect on frequency

The frequency of the wave does not change when light passes from one medium to another. This is because the frequency depends on the source of light, and not on the medium through which the light is transmitted.
03

Analyze the effect on wavelength

Wavelength (\(\lambda\)) is the distance between two successive crests or troughs in a wave. As the velocity of light decreases when it enters an optically denser medium, the wavelength also decreases. This can be seen from the wave equation: \[\lambda = \frac{v}{f}\] The frequency (\(f\)) remains constant, but the velocity (\(v\)) decreases, so the wavelength (\(\lambda\)) also decreases.
04

Analyze the effect on amplitude

Amplitude is the maximum displacement of a point on a wave from its equilibrium position. The amplitude of the wave does not change when light passes from one medium to another. This is because the amplitude depends on the energy of the wave, and not on the medium through which the light is transmitted.
05

Analyze the effect on phase

Phase is the position of a point in time on a waveform cycle. Although the phase of the light wave changes as it enters a denser medium, this is not the cause of the decrease in velocity.
06

Choose the correct answer

According to our analysis, the correct answer is (B) wavelength. The wavelength of the light wave decreases when traveling from an optically rarer medium to an optically denser medium, causing the velocity to decrease as well.

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Most popular questions from this chapter

The frequency of a light wave in a material is \(4 \times 10^{14} \mathrm{~Hz}\) and wavelength is \(5000 \AA\). The refractive index of material will be take \(\left.\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}\right)\) (A) \(1.5\) (B) \(1.7\) (C) \(1.33\) (D) None of these

A light of wavelength \(320 \mathrm{~nm}\) enters in a medium of refractive index \(1.6\) from the air of refractive index \(1.0\). The new wavelength of light in the medium will be \(\mathrm{nm}\). (A) 520 (B) 400 (C) 320 (D) 200

The distance between the first and sixth minima in the diffraction pattern of a single slit, it is \(0.5 \mathrm{~mm}\). The screen is \(0.5 \mathrm{~m}\) away from the Slit. If the wavelength of light is \(5000 \AA\), then the width of the slit will be \(\mathrm{mm}\) (D) \(1.0\) (A) 5 (B) \(2.5\) (C) \(1.25\)

A plane polarized light is incident normally on the tourmaline plate. its \(\mathrm{E}^{\rightarrow}\) vectors make an angle of \(45^{\circ}\) with the optical axis of the plate. find the percentage difference between initial and final maximum values of \(\mathrm{E}^{\rightarrow}\) vectors. (A) \(19 \%\) (B) \(92 \%\) (C) \(50 \%\) (D) \(29 \%\)

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