Physics

Question

how the light will pass and what is the angle of emergence​
how the light will pass and what is the angle of emergence​

1 Answer

  • Answer:

    The light ray goes inside with angle of refraction 30° and gets reflected at an angle 30° and then comes out refracted at an 45° with normal of third face

    Explanation:

    At the first face of prism where the light is first incident,

    we can use snell's law to determine the angle of refraction

    given refractive index of prism , μ'= √2.

    and angle if incidence , i = 45°

    now from snell's law,   sin(i) = μ sin(r),    r= angle of refraction

                                                                     μ= relative refractive index

    ⇒ sin45° = √2 sinr

    ⇒ sinr = [tex]\frac{1}{2}[/tex] ⇒ r = 30°

    Now, let top corner of prism's triangular face be A

             point where light is incident be B

             point where light gets reflected on silvered surface be C

    so that ABC forms a triangle

    now as r = 30°, ∠ABC = 90°-30° = 60°

    As sum of angles in a triangle is 180°,

    ∠ACB = 60° (since ∠BAC = 60°)

    angle of incidence on silvered face = 90°-60°= 30°

    angle of reflection = 30°

    Using same theory as above,

    the angle of incidence on third face = 30°

    Again using snell's law, sin(i) = μ sin(r)

    ⇒ sin(30) = [tex]\frac{1}{\sqrt{2} }[/tex] sin(r)

    here relative refractive index ,μ = [tex]\frac{1}{\sqrt{2} }[/tex], since light travels from prism to air

    r= 45°

    ⇒The light ray goes inside with angle of refraction 30° and gets reflected at an angle 30° and then comes out refracted at an 45° with normal of third face.