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A light ray enters from air (refractive index 1.0) into a glass slab (refractive index 1.5) at an angle of incidence of 30 degrees. What is the angle of refraction?
19.5 degrees
25.2 degrees
30 degrees
45 degrees
19.5 degrees
The angle of refraction is determined using Snell's Law, which relates the incident angle and refractive indices of the two media. Since light travels from a rarer medium (air) to a denser medium (glass), the light ray bends towards the normal, resulting in an angle of refraction smaller than the angle of incidence (30┬░).
The angle of refraction is determined using Snell's Law, which relates the incident angle and refractive indices of the two media. Since light travels from a rarer medium (air) to a denser medium (glass), the light ray bends towards the normal, resulting in an angle of refraction smaller than the angle of incidence (30┬░).
Think of a car hitting a patch of mud at an angle: the wheels entering the mud first slow down, causing the car to pivot or 'bend' toward the normal line of the boundary.
RAID: Rarer to Denser, bends towards the normal; DART: Denser to Rarer, bends away from the normal.
n1тАЛsin(i)=n2тАЛsin(r) тАФ Snell's Law
╬╝=sin(r)sin(i)тАЛ тАФ Definition of refractive index
Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, equal to the ratio of the refractive indices of the two media. Given n1тАЛsin(i)=n2тАЛsin(r), where n1тАЛ=1.0, i=30┬░, and n2тАЛ=1.5, we find sin(r)=1.51.0imessin(30┬░)тАЛ=1.50.5тАЛ=0.333. Calculating arcsin(0.333) gives approximately 19.47┬░, which rounds to 19.5┬░.
Light bends towards the normal when entering a medium with a higher refractive index.
The refractive index of air is approximately 1.0.
The refractive index of glass is typically 1.5.
Snell's law is universal for all electromagnetic waves undergoing refraction at plane interfaces.
Requires knowing the precise refractive indices of both media.
Design of lenses for optical instruments
Understanding the apparent depth of water bodies
The value sin(30┬░)=0.5.
Option B, C, and D are incorrect because they fail to satisfy the geometric constraints imposed by Snell's Law.
A is correct тАФ Based on Snell's law, sin(r)=1.5sin(30┬░)тАЛ=31тАЛ, which yields rтЙИ19.5┬░.
Always verify if the light is moving from rarer to denser or vice versa; this identifies whether the angle should increase or decrease relative to the incidence angle.