What is the angle of refraction if the angle of incidence is 40?

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When a ray of light passing through the prism is parallel to the base of the prism, it suffers a minimum deviation inside the prism and the angle of incidence becomes equal to the angle of emergence. Angle of refraction inside the material of any prism is equal to the half of the angle of prism. Hence, when the angle of refraction at first surface of the prism is 40°, and the angle of incidence is at surface of emergence then the angle of prism is 80 degrees.

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Sometimes while applying the Snell's law of refraction, you will receive the sin(Θ₂) as a value greater than 1. This is, of course, impossible - our Snell's law calculator will display the value as "NaN". If this happens, it means that all light is reflected from the boundary (this phenomenon is known as the total internal reflection).

The highest angle of incidence, for which the light is not reflected, is called the critical angle. The refracted ray travels along the boundary between both media. It means that the angle of refraction is equal to 90°. Hence, you can find the critical angle by using the following equation:

n₁sin(θ₁) = n₂sin(90°)

After simplification, n₁sin(θ₁) = n₂ * 1.

Solving for the angle of incidence, Θ₁ = arcsin(n₂/n₁).

Answer

What is the angle of refraction if the angle of incidence is 40?
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Hint: The relationship of angle of incidence and angle of refraction at interface of two media is given by Snell’s law. Snell’s law states that the ratio of the sines of the angles of incidence and refraction is equal to the reciprocal of the ratio of the indices of refraction.Use Snell’s law to find the angle of refraction.

Formula used:

Law of refraction or Snell’s law, $\dfrac{\sin {{\theta }_{1}}}{\sin {{\theta }_{2}}}=\left( \dfrac{{{\mu }_{2}}}{{{\mu }_{1}}} \right)$

Complete step-by-step answer:

When a light wave passes at some angle from one medium to another medium, its direction changes. This phenomenon is referred to as refraction.

What is the angle of refraction if the angle of incidence is 40?

Angle of incidence is defined as the angle between incident ray and normal to the interface of the media and angle of refraction is the angle between refracted ray and normal as shown in figure.Angle of incidence and angle of refraction are related by Snell’s law. Snell’s law states that the ratio of the sines of the angles of incidence and refraction is equal to the reciprocal of the ratio of the indices of refraction.$\dfrac{\sin i}{\sin r}=\left( \dfrac{{{\mu }_{2}}}{{{\mu }_{1}}} \right)$We are given that angle of incidence $i={{40}^{{}^\circ }}$ refractive index of medium 2 which is water is ${{\mu }_{2}}=\dfrac{4}{3}$. We know that the refractive index of air is ${{\mu }_{1}}=1$. Substituting these values in Snell’s law, we have$\dfrac{\sin {{40}^{{}^\circ }}}{\sin r}=\dfrac{4/3}{1}$On rearranging and solving the above equation, we get$\sin r=\dfrac{3}{4}\sin {{40}^{{}^\circ }}=\dfrac{3}{4}\times 0.643\approx 0.48$Therefore, angle of refraction is $r={{\sin }^{-1}}\left( 0.48 \right)$

Note: The law of refraction or Snell’s law is valid for all pairs of media at the point of incidence. Incident ray, normal and refracted ray lie in the same plane.

Refractive index of a medium is a unitless quantity. It is also defined as the ratio of velocity of wave in the medium to velocity of wave in vacuum. Refractive index of air or free space is unity.

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