Refraction of Light — Maharashtra (SSC) Class 10 Science Solutions (Free)

Refraction: Bending of light when it travels from one medium to another of different optical density. Laws: (1) Incident ray, refracted ray, and normal lie in same plane, (2) Snell's law: n1 sin(theta1) = n2 sin(theta2), where n is refractive index, theta is angle with normal. Light bends toward normal when entering denser medium (smaller angle), away from normal in rarer medium (larger angle). Refractive index = speed of light in vacuum / speed in medium.

Step 1: Given n1 = 1.33 (water), theta1 = 30 degrees, n2 = 1 (air) Step 2: Use Snell's law: n1 sin(theta1) = n2 sin(theta2) Step 3: 1.33 x sin(30) = 1 x sin(theta2) Step 4: 1.33 x 0.5 = sin(theta2) Step 5: sin(theta2) = 0.665, so theta2 = 41.6 degrees Answer: Angle of refraction is 41.6 degrees. Light bends away from normal going from denser to rarer medium.

Refractive index: Ratio of speed of light in vacuum to speed of light in medium. Formula: n = c/v, where c = 3 x 10^8 m/s (speed in vacuum), v = speed in medium. Refractive index is dimensionless and always greater than 1 for denser media. Higher refractive index means light travels slower in that medium. Calculation: n = (3 x 10^8) / (2 x 10^8) = 1.5. Glass with n=1.5 is commonly used in lenses because it refracts light significantly.

When light from pencil travels from water (denser, n=1.33) to air (rarer, n=1), it refracts away from normal at the surface. Light undergoes refraction at water-air interface, bending away from normal. When this refracted light reaches our eye, our brain traces it backward assuming straight-line path, making the pencil appear bent or shifted. The apparent depth of water is less than actual depth due to this refraction. The amount of bending depends on angle of incidence and refractive indices of both media.

Critical angle: Angle of incidence in a denser medium at which angle of refraction becomes 90 degrees in rarer medium. Formula: sin(theta_c) = n2/n1. For angle > critical angle, refracted ray doesn't exist; light is completely reflected back into the denser medium. Total internal reflection: Complete reflection of light back into medium when light travels from denser to rarer medium at angle greater than critical angle. No light escapes the denser medium. Used in fiber optics, diamonds (high refractive index), periscopes. Critical angle for glass-air is about 42 degrees.

Step 1: Formula for critical angle: sin(theta_c) = n2/n1 Step 2: n1 = 1.5 (glass), n2 = 1 (air) Step 3: sin(theta_c) = 1/1.5 = 0.667 Step 4: theta_c = sin^(-1)(0.667) = 41.8 degrees Answer: Critical angle is 41.8 degrees. For angles of incidence greater than 41.8 degrees, light undergoes total internal reflection. Diamonds with n=2.42 have critical angle of 24.4 degrees, making them sparkle.

Diamond has higher refractive index (n=2.42) compared to glass (n=1.5). Higher refractive index means greater bending of light and lower critical angle. Critical angle for diamond = 24.4 degrees, much smaller than glass's 41.8 degrees. Light entering diamond undergoes total internal reflection at smaller angles, reflecting more light internally. Multiple internal reflections concentrate light toward observer, creating brilliance and sparkle. Diamond's high refractive index and small critical angle trap and reflect more light, making it appear brighter and more colorful than glass or other gemstones.