To find the angle through which the ray is minimally deviated in the prism, we can use Snell's Law.
According to Snell's Law, the angle of incidence (i) and the angle of refraction (r) are related by the equation:
n1 × sin(i) = n2 × sin(r),
where n1 is the refractive index of the medium from which the light is coming (in this case, air), and n2 is the refractive index of the medium into which the light is entering (in this case, the prism).
Since the refractive index of air is approximately 1, we can rewrite the equation as:
sin(i) = (n2 / n1) × sin(r).
For an equilateral triangular prism, the angle of minimum deviation occurs when the angle of incidence is equal to the angle of emergence (e) and the emergent ray is parallel to the base of the prism. In this case, the angle of incidence is 90 degrees - (e/2).
Using the given refractive index of 3/2, we can substitute the values into the equation:
sin(90 - e/2) = (3/2) × sin(e).
To solve for e, we can use a scientific calculator or a trigonometric identity. By rearranging the equation, we get:
sin(e) = (2/3) × sin(90 - e/2).
We can then calculate the approximate value of e using a scientific calculator. By inputting the equation t0o calculate for the angle in degrees:
e ≈ 42.0°.
Therefore, the correct answer is C. 42.0°.
A ray of light is incident on an equilateral triangular glass prism of refractive index 3/2, Calculate the angle through which the ray is minimally deviated in the prism
A. 30.0∘
B. 37.2∘
C. 42.0∘
D. 48.6∘
1 answer