A light ray travelling in a transparent glass block of refractive index 1.5 strikes a planar boundary with a liquid of refractive index n . When the ray is incident at the exact critical angle for total internal reflection, the angle between the incident ray and the internally reflected ray is found to be 106^ . If (53^ ) = 4 5 , the value of 10n is ________.

Step-by-step solution

According to the law of reflection, the angle of incidence is equal to the angle of reflection. Given the angle between the incident ray and the internally reflected ray is 106^ , the angle of incidence is i = 106^ 2 = 53^ . For the critical angle condition, the refracted ray grazes the boundary, so the angle of refraction is 90^ . Applying Snell's law at the glass-liquid interface: _ glass i = n 90^ 1.5 53^ = n 1 1.5 4 5 = n n = 1.2 Therefore, 10n = 10 1.2 = 12 . Answer: 12