A prism can produce a minmum deviation `delta` in a the beam. If three such prisms are combined, the minimum deviation that can be produced in this beam is

Options

A. 0
B. `2delta`
C. `delta`
D. `3 delta

Answer

To solve the problem, we need to analyze the behavior of light passing through multiple prisms and how their minimum deviations interact. Here's a step-by-step solution:

### Step 1: Understand the Minimum Deviation in a Single Prism
A single prism can produce a minimum deviation, denoted as \( \delta \), when light passes through it. This deviation is a characteristic of the prism's angle and the refractive index of the material.

**Hint:** Recall that the minimum deviation occurs when light enters and exits the prism symmetrically.

### Step 2: Analyze the Effect of Multiple Prisms
When multiple prisms are combined, the light passing through them will experience deviations based on how each prism interacts with the light.

**Hint:** Consider how light behaves when it passes through multiple optical elements in sequence.

### Step 3: Consider the Sequence of Prisms
Let’s denote the three prisms as Prism 1, Prism 2, and Prism 3. When light passes through these prisms:
- Prism 1 causes a deviation of \( \delta \).
- Prism 2, which is placed next, will cause the light to converge back to white light, effectively introducing a deviation of \( -\delta \) (since it reverses the dispersion).
- Prism 3 will again cause a deviation of \( \delta \) as it disperses the light once more.

**Hint:** Think about how the light is transformed by each prism in the sequence.

### Step 4: Calculate the Net Deviation
Now, we can calculate the net deviation:
- Deviation from Prism 1: \( +\delta \)
- Deviation from Prism 2: \( -\delta \)
- Deviation from Prism 3: \( +\delta \)

The net deviation can be calculated as follows:
\[ \text{Net Deviation} = \delta + (-\delta) + \delta = \delta \]

**Hint:** Combine the deviations algebraically, paying attention to the signs.

### Step 5: Conclusion
The minimum deviation that can be produced by the combination of three prisms is \( \delta \).

**Final Answer:** The correct option is \( \delta \) (Option 3).

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