The power of a convex lens is `2` dioptres. Its power is to be reduced to `1.5` dioptres, by putting another lens in combination with it. Which of the following lens will serve the purpose ?

Options

A. A concave lens of focal length `2` m.
B. A concave lens of focal length `4` m.
C. A convex lens of focal length `2` m.
D. A concave lens of focal length `1` m.

Explanation

To solve the problem step by step, we need to find the appropriate lens that will reduce the power of a convex lens from 2 diopters to 1.5 diopters.

### Step 1: Understand the Given Information
We have a convex lens with a power \( P_1 = 2 \) diopters. We want to reduce this power to \( P = 1.5 \) diopters by combining it with another lens.

### Step 2: Use the Formula for Combined Power
The formula for the combined power \( P \) of two lenses in combination is given by:
\[ P = P_1 + P_2 \]
where \( P_2 \) is the power of the second lens.

### Step 3: Rearranging the Formula
We can rearrange the formula to find \( P_2 \):
\[ P_2 = P - P_1 \]

### Step 4: Substitute the Known Values
Substituting the known values into the equation:
\[ P_2 = 1.5 \, \text{diopters} - 2 \, \text{diopters} \]
\[ P_2 = -0.5 \, \text{diopters} \]

### Step 5: Interpret the Result
The negative sign indicates that the second lens is a concave lens. The magnitude of the power is \( 0.5 \) diopters.

### Step 6: Find the Focal Length of the Second Lens
The power \( P \) of a lens is related to its focal length \( f \) by the formula:
\[ P = \frac{1}{f} \]
Thus, for the second lens:
\[ P_2 = -0.5 \, \text{diopters} \implies f_2 = \frac{1}{P_2} = \frac{1}{-0.5} = -2 \, \text{meters} \]

### Step 7: Conclusion
The second lens is a concave lens with a focal length of \( 2 \) meters.

### Final Answer
The lens that will serve the purpose is a **concave lens with a focal length of 2 meters**.

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