A ray of light is incident at an angle of 30° on a glass prism of refractive index 1.5 . calculate the angle through which the ray is minimally deviated in the prism.(the medium surrounding the prism is air)

and your work is? Snell's law is pretty straight forward.

To calculate the angle through which the ray is minimally deviated in the prism, you can use Snell's law and the formula for the angle of deviation.

1. Snell's Law relates the angles of incidence and refraction to the refractive indices of two media:

n₁ * sin(angle of incidence) = n₂ * sin(angle of refraction)

Given:
n₁ = refractive index of air = 1
n₂ = refractive index of the glass prism = 1.5
angle of incidence = 30°

Plugging these values into the equation, we have:

1 * sin(30°) = 1.5 * sin(angle of refraction)

2. We know that the angle of deviation (d) is related to the angle of incidence (i) and angle of refraction (r) by the formula:

d = (i + r) - 180°

Since we want to find the angle through which the ray is "minimally deviated," we can assume that the angle of incidence (i) is equal to the angle of refraction (r).

3. Therefore, let's set i = r = x, where x is the angle we need to find.

Plugging this into equation (1):

1 * sin(30°) = 1.5 * sin(x)

Simplifying, we have:

sin(30°) = 1.5 * sin(x)

Now, solve for x.

sin(x) = sin(30°) / 1.5

x = arcsin(sin(30°) / 1.5)

Using a scientific calculator, evaluate the arcsin to find the value of x:

x ≈ 19.47°

So, the angle through which the ray is minimally deviated in the prism is approximately 19.47°.

To calculate the angle through which the ray is minimally deviated in the prism, you can use Snell's law of refraction, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the speeds of light in the two media. Here's how you can calculate the angle:

Step 1: Determine the angle of incidence and refractive index
Given that the angle of incidence is 30° and the refractive index of the prism is 1.5, you have:
Angle of incidence (i) = 30°
Refractive index of prism (n) = 1.5

Step 2: Calculate the angle of refraction inside the prism
Since the medium surrounding the prism is air (since the refractive index of air is approximately 1), you can use Snell's law to calculate the angle of refraction inside the prism.
Snell's law: n₁ * sin(i) = n₂ * sin(r)
where n₁ is the refractive index of the medium of incidence (which is air) and n₂ is the refractive index of the medium of refraction (which is the prism).

Since n₁ = 1 and n₂ = 1.5, you can substitute these values into Snell's law:
1 * sin(30°) = 1.5 * sin(r)

Step 3: Solve for the angle of refraction
Using a scientific calculator, solve the equation for the angle of refraction (r).

sin(r) = (1/1.5) * sin(30°)
sin(r) = 0.66667 * 0.5
sin(r) = 0.33333

To find the angle, take the inverse sine (sin⁻¹) of 0.33333:
r ≈ sin⁻¹(0.33333)
r ≈ 19.47° (approximately)

So, the angle of refraction inside the prism is approximately 19.47°.

Step 4: Calculate the angle through which the ray is minimally deviated
The angle through which the ray is minimally deviated in the prism is the difference between the angle of incidence and the angle of refraction. Therefore:
Angle of deviation = i - r
Angle of deviation = 30° - 19.47°
Angle of deviation ≈ 10.53° (approximately)

Hence, the ray is minimally deviated in the prism by approximately 10.53°.