A ray of light is incident at an angle of 30° on a glass prime of refractive index 1.5 . calculate the angle through which the ray is minimally deviated in the prime.
Snell's law applies. The angle has to be measured from the normal, I assume by "prime" you mean normal.
To calculate the angle through which the ray is minimally deviated in the prism, we need to understand how refraction works.
Here's a step-by-step explanation of how to calculate the angle of minimal deviation in a prism:
1. Draw a ray diagram: Start by drawing a diagram to visualize the situation. Draw the incident ray coming from air and entering the prism at an angle of 30°.
Incident ray
\
\ |
____\__|____
| |
n1 | |
| Prism |
| |
|______________|
Normal
2. Identify the relevant angles: In this case, we have the angle of incidence (i) which is 30°, and the refractive index of the prism (n2) which is 1.5.
3. Use Snell's Law to find the angle of refraction: Snell's Law states that n1*sin(i) = n2*sin(r), where n1 and n2 are the refractive indices of the initial and final medium, i is the angle of incidence, and r is the angle of refraction. Since the incident ray is coming from air (n1 ≈ 1), we can rewrite the equation as sin(i) = n2*sin(r).
sin(30°) = 1.5*sin(r)
sin(r) = sin(30°) / 1.5
sin(r) ≈ 0.5 / 1.5
sin(r) ≈ 0.3333
Using a calculator or referencing a sine table, we find that the angle r is approximately 19.47°.
4. Calculate the angle of deviation: The angle of deviation (D) can be defined as D = (i + r - A), where A is the angle at which the refracted ray emerges from the prism. However, in the case of minimal deviation, the angle of incidence and angle of emergence are equal (i.e., A = i).
Therefore, the angle of deviation (D) becomes D = (i + r - i) = r.
So, the angle of deviation for minimal deviation is approximately 19.47°.
Therefore, the ray is minimally deviated by an angle of approximately 19.47° in the glass prism.