A ray of light makes a glancing angle of incidence of 60° with a flat glass surface. Given that the critical angle for glass is 42°, determine the angle of refraction r.

Part 1: Angle of refraction Speed of light in air: c = 3 × 10^8 m/s Speed of light in glass: v_g = 2 × 10^8 m/s Step 1: Refractive index of glass n_g = (c)/(v_g) Substitute values: n_g = 3 × 10^82 × 10^8 = 1.5 Step 2: Snell's law n_air i = n_g r Substitute n_air = 1 , i = 45^ : 1 · 45^ = 1.5 r r = ( 45^)/(1.5) Step 3: Compute 45^ = sqrt(2)2 r = sqrt(2)21.5 = sqrt(2)2 × (2)/(3) = sqrt(2)3 r = (1.414)/(3) = 0.4713 Step 4: Angle of refraction r = ^-1(0.4713) ≈ 28^ Final answer: r = 28^ Part 2: Magnifying power of microscope Focal length of objective: f_o = 0.50 cm Focal length of eyepiece: f_e = 2.5 cm Tube length: L = 16.0 cm Least distance of distinct vision: D = 25 cm Step 1: Image distance for objective (normal adjustment) L = v_o + f_e Substitute values: 16.0 = v_o + 2.5 v_o = 16.0 - 2.5 = 13.5 cm Step 2: Object distance for objective (lens formula) (1)/(v_o) - (1)/(u_o) = (1)/(f_o) (1)/(u_o) = (1)/(f_o) - (1)/(v_o) Substitute values: (1)/(u_o) = (1)/(0.50) - (1)/(13.5) = 2 - (2)/(27) (1)/(u_o) = (54)/(27) - (2)/(27) = (52)/(27) u_o = (27)/(52) cm Step 3: Lateral magnification by objective m_o = (v_o)/(|u_o|) Substitute values: m_o = (13.5)/(27)52 = 13.5 × (52)/(27) 13.5 = (27)/(2) m_o = (27)/(2) × (52)/(27) = (52)/(2) = 26 Step 4: Angular magnification by eyepiece (image at infinity) m_e = (D)/(f_e) Substitute values: m_e = (25)/(2.5) = 10 Step 5: Total magnification m = m_o × m_e Substitute values: m = 26 × 10 = 260 Final answer: m = 260