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:

• 6°
• 8°
• 10°
• 4°

To find the refracting angle of the second prism that, when combined with the first prism, produces dispersion without deviation, we can use the formula for the condition of no deviation in prisms:

Formula for No Deviation

The condition for no deviation in a combination of two prisms is given by:

n1 * A1 = n2 * A2

Where:

• n1 = refractive index of the first prism
• A1 = refracting angle of the first prism
• n2 = refractive index of the second prism
• A2 = refracting angle of the second prism

Given Values

For the first prism:

• Refracting angle (A1) = 10°
• Refractive index (n1) = 1.42

For the second prism:

• Refractive index (n2) = 1.7
• Refracting angle (A2) = ?

Calculation

Substituting the known values into the formula:

1.42 * 10° = 1.7 * A2

Now, solving for A2:

A2 = (1.42 * 10°) / 1.7

A2 ≈ 8.35°

Choosing the Closest Option

The closest option to 8.35° from the given choices (6°, 8°, 10°, 4°) is:

8°

Thus, the refracting angle of the second prism should be 8°.