A pair of nicols is used to polarise light. The analyser is rotated through an angle of `60^@`. Determine the reduction in maximum value of light transmitted.

Answer

To solve the problem of determining the reduction in the maximum value of light transmitted when the analyzer is rotated through an angle of \(60^\circ\), we can follow these steps:

### Step 1: Understand the Setup
We have a pair of Nicol prisms (polarizers). The first Nicol polarizes the incoming light, and the second Nicol acts as an analyzer. The angle between the transmission axes of the two polarizers is crucial for determining the intensity of the transmitted light.

### Step 2: Apply Malus's Law
Malus's Law states that when polarized light passes through a polarizer (analyzer), the intensity \(I\) of the transmitted light is given by:
\[ I = I_0 \cos^2(\theta) \]
where:
- \(I_0\) is the initial intensity of the polarized light,
- \(\theta\) is the angle between the light's polarization direction and the axis of the analyzer.

### Step 3: Identify the Angle
In this case, the analyzer is rotated through an angle of \(60^\circ\). Thus, we can set \(\theta = 60^\circ\).

### Step 4: Calculate the Transmitted Intensity
Using Malus's Law, we can calculate the transmitted intensity \(I\) after the analyzer is rotated:
\[ I = I_0 \cos^2(60^\circ) \]
We know that:
\[ \cos(60^\circ) = \frac{1}{2} \]
Thus:
\[ \cos^2(60^\circ) = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \]
Substituting this back into the equation for \(I\):
\[ I = I_0 \cdot \frac{1}{4} = \frac{I_0}{4} \]

### Step 5: Determine the Reduction in Intensity
The maximum value of light transmitted (when the analyzer is aligned with the polarizer) is \(I_0\). After the analyzer is rotated:
\[ I = \frac{I_0}{4} \]
The reduction in intensity can be calculated as:
\[ \text{Reduction} = I_0 - I = I_0 - \frac{I_0}{4} = \frac{3I_0}{4} \]

### Final Answer
Thus, the reduction in the maximum value of light transmitted when the analyzer is rotated through an angle of \(60^\circ\) is:
\[ \frac{3I_0}{4} \]

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