Answer:

Introduction:
In this question, a ray of light is incident on a face of an equilateral triangle at an incident angle of 50. At this minimum deviation occurs. We have to find out the deviation angle.

Explanation:
To find the deviation angle, we can use the formula for the deviation angle of a prism:

A = (μ - 1)δ

where A is the deviation angle, μ is the refractive index of the prism, and δ is the angle of minimum deviation.

For an equilateral triangle prism, the angle of incidence and the angle of emergence are equal, so we can use the following formula to find the angle of minimum deviation:

δ = (2/3)α

where α is the angle of the prism (60 degrees for an equilateral triangle).

Using the given incident angle of 50 degrees, we can find the angle of refraction using Snell's law:

sin i / sin r = n1 / n2

where i is the angle of incidence, r is the angle of refraction, n1 is the refractive index of air (approximately 1), and n2 is the refractive index of the prism.

Assuming the refractive index of the prism is 1.5 (typical for glass), we get:

sin 50 / sin r = 1 / 1.5
sin r = sin 50 / 1.5 = 0.4667
r = sin^-1(0.4667) = 28.6 degrees

Now we can use the formulas above to find the deviation angle:

δ = (2/3)α = 40 degrees (approximately)
μ = (sin[(δ+A)/2]) / sin(α/2) = 1.5 (approximately)
A = (μ - 1)δ = 20 degrees (approximately)

Therefore, the deviation angle is approximately 40 degrees.

Conclusion:
In conclusion, the deviation angle for a ray of light incident on a face of an equilateral triangle prism at an incident angle of 50 degrees is approximately 40 degrees.