Question

The figures below show a piece of glass which is in air. A beam of white light consists of various colors with wavelengths ranging λviolet = 400 nm for violet light up to λred = 700 nm for red light is incident on the vertical surface between the glass and air. The light makes an angle of incidence of θ1 = 27° at the interface; the index of refraction for the glass is nviolet = 1.57 for violet light and nred = 1.44 for red light.(a) Once the light has passed into the glass, which will be higher, the violet light or the red (try to answer this before making any calculations)? - the violet light or the red light or more information is needed

(b)What will be the angle which violet light makes with the horizontal after the beam passes over into glass?
(c) What will be the angle which red light makes with the horizontal after the beam passes over into glass?
(d) Once the light has passed into the air, which will be higher, the violet light or the red (try to answer this before making any calculations)? -the violet light, the red light or more information is needed.

Answer 1

red light deviates a greater amount.

Step-by-step explanation:

Refractive problems should be solved in the equation

n1 sin θ1 = n2 sin θ2

Where n1 and n2 are the indexes of refraction of the material, for air it is n1 = 1, and θ are the angles of incidencence and refraction

a) Let's try to analyze the incidence of white light, the index of refraction of violet light is larger than the index of red light, therefore, if the other parameters: air, angle of incidence are maintained the angle of Violet light transmission should be less, or what is the same the red light deviates a greater amount.

b and c) We calculate the transmission angle for the two lights

Violet

sin θ2 = n1/n2 sin θ1

sin θ2 = 1/1.57 sin 27

sin θ2 = 0.289

θ2 = sin⁻¹ 0.289

θ2 = 16.8º

Red

sin θ3 = 1 / 1.44 sin 27 = 0.315

θ3 = 18.4º

In optics the angles are measured with respect to the normal one that is a line perpendicular to the surface (glass), if the angle with respect to the horizontal is desired we must subtract 90º

φ1 = 90 + θ1 = 90 -16.8

φ1 = 73.2º

φ2 =90 - θ2 = 90 -18.4

φ2 = 71.6º

The angles φ are with respect to the horizontal

d) When it passes from the glass to the air it has the opposite case, it sees a medium with a higher refractive index to a lower one, so the rays have the opposite behavior, so that the ray that least deviates is red and the one that most detours is the violet

the thickness of the glass plate is needed to calculate this information