A thin prism having refracting angle `10^(@)` is made of glass of refracting index `1.42`. This prism is combined with another thin prism of glass of refractive index `1.7`. This combination produces dispersion without deviation. The refracting angle of second prism should be `:`

Options

A. `4^(@)`
B. `6^(@)`
C. `8^(@)`
D. `10^(@)`

Explanation

To solve the problem of finding the refracting angle of the second prism, we can follow these steps:

### Step 1: Understand the condition for dispersion without deviation
The condition for dispersion without deviation in a combination of two prisms is given by the formula:
\[ A_1 (\mu_1 - 1) = A_2 (\mu_2 - 1) \]
where:
- \( A_1 \) is the refracting angle of the first prism,
- \( \mu_1 \) is the refractive index of the first prism,
- \( A_2 \) is the refracting angle of the second prism,
- \( \mu_2 \) is the refractive index of the second prism.

### Step 2: Identify the known values
From the problem, we have:
- \( A_1 = 10^\circ \)
- \( \mu_1 = 1.42 \)
- \( \mu_2 = 1.7 \)

### Step 3: Substitute the known values into the formula
We can substitute the known values into the dispersion condition:
\[ 10 (\mu_1 - 1) = A_2 (\mu_2 - 1) \]
This becomes:
\[ 10 (1.42 - 1) = A_2 (1.7 - 1) \]

### Step 4: Simplify the equation
Now, simplify the left and right sides:
\[ 10 (0.42) = A_2 (0.7) \]
This simplifies to:
\[ 4.2 = A_2 (0.7) \]

### Step 5: Solve for \( A_2 \)
To find \( A_2 \), divide both sides by \( 0.7 \):
\[ A_2 = \frac{4.2}{0.7} \]
Calculating this gives:
\[ A_2 = 6^\circ \]

### Conclusion
The refracting angle of the second prism should be \( 6^\circ \).

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