Three prisms 1, 2 and 3 have A = 6°, but refractive indices are 1.4, 1.5, 1.6 and their angles of deviation are `delta_(1) ,delta_(2) delta_(3)` respectively. Then

Options

A. `delta_(3)gtdelta_(2)gtdelta_(1)`
B. `delta_(1)gtdelta_(2)gtdelta_(3)`
C. `delta_(2)gtdelta_(1)gtdelta_(3)`
D. `delta_(1)=delta_(2)=delta_(3)`

Answer

To solve the problem, we need to find the order of angles of deviation for the three prisms based on their refractive indices. The formula for the angle of deviation (δ) for a prism is given by:

\[ \delta = (\mu - 1) \cdot A \]

where:
- \(\mu\) is the refractive index of the prism,
- \(A\) is the angle of the prism.

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- For all three prisms, the angle of the prism \(A = 6^\circ\).
- Refractive indices:
- Prism 1: \(\mu_1 = 1.4\)
- Prism 2: \(\mu_2 = 1.5\)
- Prism 3: \(\mu_3 = 1.6\)

**Step 2: Calculate \(\delta\) for each prism using the formula.**

For Prism 1:
\[ \delta_1 = (\mu_1 - 1) \cdot A = (1.4 - 1) \cdot 6^\circ = 0.4 \cdot 6^\circ = 2.4^\circ \]

For Prism 2:
\[ \delta_2 = (\mu_2 - 1) \cdot A = (1.5 - 1) \cdot 6^\circ = 0.5 \cdot 6^\circ = 3.0^\circ \]

For Prism 3:
\[ \delta_3 = (\mu_3 - 1) \cdot A = (1.6 - 1) \cdot 6^\circ = 0.6 \cdot 6^\circ = 3.6^\circ \]

**Step 3: Compare the angles of deviation.**
- \(\delta_1 = 2.4^\circ\)
- \(\delta_2 = 3.0^\circ\)
- \(\delta_3 = 3.6^\circ\)

**Step 4: Determine the order of angles of deviation.**
From the calculations:
- \(\delta_3 > \delta_2 > \delta_1\)

Thus, the order of angles of deviation is:
\[ \delta_3 > \delta_2 > \delta_1 \]

### Final Answer:
The order of angles of deviation is \(\delta_3 > \delta_2 > \delta_1\).

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