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Chapter 16: Problem 2226

If thin prism of \(5^{\circ}\) gives a deviation of \(2^{\circ}\) then the refractive index of material of prism is (A) \(1.4\) (B) \(1.5\) (C) \(1.6\) (D) \(1.0\)

Short Answer

Expert verified
The refractive index of the material of the prism is approximately \(1.4\) (option A).

Step by step solution

01

Identify given values

We are given the prism angle, \(A=5^{\circ}\), and the deviation, \(δ=2^{\circ}\).
02

Use the deviation in a thin prism formula

To find the refractive index \(n\) of the material, we will use the formula \(δ = (n-1)A\). Plug the given values into the formula: \( 2 = (n - 1)(5) \).
03

Solve for the refractive index, n

Now, solve for \(n\) from the equation: \( 2 = 5(n-1) \) First, divide both sides by 5: \( \frac{2}{5} = n - 1 \) Next, add 1 to both sides of the equation: \( n = \frac{2}{5} + 1 = \frac{7}{5} \) Finally, convert the fraction to a decimal (rounded to one decimal place): \( n \approx 1.4 \) Therefore, the refractive index of the material of the prism is approximately 1.4, which corresponds to option (A).

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