All components of the electromagnetic spectrum in vacuum have the same

151. All components of the electromagnetic spectrum in vacuum have the same In a vacuum, all components of the electromagnetic spectrum (radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays) travel at the same speed, which is the speed of light, c. Their frequencies, wavelengths, and energies, however, differ. The correct option is (4). 4 152. The focal length of a convex lens of refractive index (3)/(2) is 20 cm in air. Focal length of this lens when immersed in a liquid of refractive index of (5)/(2) will be Step 1: Write the lens maker's formula. The lens maker's formula relates the focal length of a lens to its refractive index, the refractive index of the surrounding medium, and its radii of curvature: (1)/(f) = ((n_l)/(n_m) - 1) ((1)/(R_1) - (1)/(R_2)) where f is the focal length, n_l is the refractive index of the lens material, n_m is the refractive index of the surrounding medium, and R_1, R_2 are the radii of curvature of the lens surfaces. Step 2: Use the given information for the lens in air to find the term related to radii of curvature. Given: Refractive index of lens n_l = (3)/(2). Focal length in air f_air = 20 cm. Refractive index of air n_air = 1. Substitute these values into the formula: (1)/(20) = ((3/2)/(1) - 1) ((1)/(R_1) - (1)/(R_2)) (1)/(20) = ((3)/(2) - 1) ((1)/(R_1) - (1)/(R_2)) (1)/(20) = ((1)/(2)) ((1)/(R_1) - (1)/(R_2)) Solving for the term ((1)/(R_1) - (1)/(R_2)): ((1)/(R_1) - (1)/(R_2)) = (2)/(20) = (1)/(10) Step 3: Calculate the focal length when immersed in the liquid. Given: Refractive index of liquid n_liquid = (5)/(2). Let the focal length in liquid be f_liquid. Substitute n_l, n_liquid, and the calculated ((1)/(R_1) - (1)/(R_2)) into the lens maker's formula: (1)/(f_liquid) = ((3/2)/(5/2) - 1) ((1)/(10)) (1)/(f_liquid) = ((3)/(5) - 1) ((1)/(10)) (1)/(f_liquid) = ((3-5)/(5)) ((1)/(10)) (1)/(f_liquid) = (-(2)/(5)) ((1)/(10)) (1)/(f_liquid) = -(2)/(50) = -(1)/(25) Therefore, the focal length in the liquid is: f_liquid = -25 cm The negative sign indicates that the convex lens behaves as a concave lens when immersed in a medium with a higher refractive index than the lens material. The correct option is (2). 2 153. Three prisms A, B and C have the prism angle 6^ but their refractive indices are respectively 1.4, 1.6 and 1.8. If _1, _2, _3 be their respective angles of deviation then Step 1: Recall the formula for the angle of deviation for a small angle prism. For a prism with a small angle A, the angle of deviation is given by: = (n-1)A where n is the refractive index of the prism material. Step 2: Calculate the angle of deviation for each prism. Given: Prism angle A = 6^ for all three prisms. For prism A: n_A = 1.4 _1 = (1.4 - 1) × 6^ = 0.4 × 6^ = 2.4^ For prism B: n_B = 1.6 _2 = (1.6 - 1)