A light of ray is incident at an angle of 58degrees on the plane surface of a block of glass of refractive index 1.60. Some light is reflected on the other side of the normal att he same angle as the angle of incidence.
Find:
a.the angle between the light reflected from the surface and the light refracted into the glass
b.the deviation of the refracted ray
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To solve this problem, we can use the laws of reflection and refraction.
a. The angle between the light reflected from the surface and the light refracted into the glass can be found using the law of reflection. According to this law, the angle of incidence is equal to the angle of reflection. Therefore, the angle between the reflected light and the refracted light will also be 58 degrees.
b. The deviation of the refracted ray can be found using Snell's law. According to Snell's law, the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities of light in the two media. Mathematically, it can be written as:
sin(angle of incidence) / sin(angle of refraction) = speed of light in medium 1 / speed of light in medium 2
In this case, the speed of light in a vacuum or air is essentially the same, so we can simplify the equation to:
sin(angle of incidence) / sin(angle of refraction) = 1.60 (refractive index of glass)
Let's solve this equation to find the angle of refraction. Rearranging the equation and substituting the given values:
sin(58 degrees) / sin(angle of refraction) = 1.60
sin(angle of refraction) = sin(58 degrees) / 1.60
Using a calculator, we find sin(angle of refraction) ≈ 0.5723.
Now, we can take the inverse sine of 0.5723 to find the angle of refraction:
angle of refraction ≈ sin^(-1)(0.5723)
Using a calculator, we find the angle of refraction ≈ 34.77 degrees.
Since the ray is bending towards the normal as it enters the glass, the deviation of the refracted ray can be calculated by subtracting the angle of incidence from the angle of refraction:
Deviation = angle of refraction - angle of incidence
= 34.77 degrees - 58 degrees
≈ -23.23 degrees
Therefore, the deviation of the refracted ray is approximately -23.23 degrees.