Question 1

Q1: 10.1 Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected,...

Accepted Answer

Given: - Wavelength of monochromatic light in air, λ_air = 589 nm = 589 × 10⁻⁹ m - Refractive index of water, n_water = 1.33 - Speed of light in vacuum (and air), c = 3.0 × 10⁸ m/s First, let's calculate the frequency of the incident light. The frequency of light depends only on the source and does...

Question 2

Q2: 10.2 What is the shape of the wavefront in each of the following cases: (a) Light diverging from a point source. (b) Light emerging out of a convex le...

Accepted Answer

A wavefront is defined as the locus of all points that are in the same phase of vibration. (a) Light diverging from a point source. For a point source emitting light uniformly in all directions in an isotropic medium, the light waves travel outwards with the same speed in all directions. The locus o...

Question 3

Q3: 10.3 (a) The refractive index of glass is 1.5 . What is the speed of light in glass? (Speed of light in vacuum is 3.0 × 10⁸ m s⁻¹) (b) Is the speed of...

Accepted Answer

(a) Speed of light in glass Given: - Refractive index of glass, n_g = 1.5 - Speed of light in vacuum, c = 3.0 × 10⁸ m/s The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v). n = c / v Rearranging for the speed of lig...

Question 4

Q4: 10.4 In a Young's double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bri...

Accepted Answer

Given: - Separation between the slits, d = 0.28 mm = 0.28 × 10⁻³ m - Distance of the screen from the slits, D = 1.4 m - The distance between the central bright fringe (n=0) and the fourth bright fringe (n=4) is 1.2 cm = 1.2 × 10⁻² m In a Young's double-slit experiment, the position (x_n) of the n-th...

Question 5

Q5: 10.5 In Young's double-slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path differenc...

Accepted Answer

The intensity (I) at a point on the screen in a Young's double-slit experiment is given by: I = 4I₀ cos²(φ/2) where I₀ is the intensity from a single slit and φ is the phase difference between the waves from the two slits. The phase difference (φ) is related to the path difference (Δx) by the formul...

Question 6

Q6: 10.6 A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young's double-slit experiment. (a)...

Accepted Answer

Given: - First wavelength, λ₁ = 650 nm = 650 × 10⁻⁹ m - Second wavelength, λ₂ = 520 nm = 520 × 10⁻⁹ m For this problem, we will assume the experimental setup is the same as in question 10.4: - Slit separation, d = 0.28 mm = 0.28 × 10⁻³ m - Screen distance, D = 1.4 m The position of the n-th bright f...

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