Calculate the refractive index of minimum of a 60 degree triangular glass prism (refractive index of glass is 1.5)
The Correct Answer and Explanation is:
To calculate the refractive index of the minimum deviation of a 60-degree triangular glass prism, we use the following formula:n=sin(A+D2)sin(A2)n = \frac{\sin\left(\frac{A + D}{2}\right)}{\sin\left(\frac{A}{2}\right)}n=sin(2A)sin(2A+D)
Where:
- nnn is the refractive index of the prism,
- AAA is the angle of the prism (60° in this case),
- DDD is the angle of minimum deviation, which we need to determine.
Step-by-Step Solution:
- Understand the Problem:
The refractive index of the glass is given as 1.5. However, we are required to find the refractive index at the condition of minimum deviation. In the case of minimum deviation, the light passes symmetrically through the prism, meaning the angle of incidence equals the angle of emergence. - Equation for Minimum Deviation:
For a prism, the relationship between the angle of the prism AAA, the refractive index nnn, and the angle of minimum deviation DDD is derived from Snell’s law. - Using the Formula for the Refractive Index:
From the formula above, we can determine nnn for minimum deviation by substituting the known values:- Angle of the prism A=60∘A = 60^\circA=60∘,
- The refractive index of the glass nglass=1.5n_{\text{glass}} = 1.5nglass=1.5.
n=sin(60∘+D2)sin(60∘2)n = \frac{\sin\left(\frac{60^\circ + D}{2}\right)}{\sin\left(\frac{60^\circ}{2}\right)}n=sin(260∘)sin(260∘+D)
Since the refractive index for the glass is given as 1.5, we can solve for the value of DDD and plug it into the equation. Based on experiments or known data, the angle of minimum deviation DDD for a triangular prism is usually approximated.
- Conclusion:
The refractive index at the minimum deviation condition, using the above equation and approximating DDD, would be 1.5.
