If R1 and R2 are the radii of curvature of a double convex lens. The largest power will be for

Options

A. `R_(1)=oo,R_(2)=10cm`
B. `R_(1)=10cm,R_(2)=oo`
C. `R_(1)=10cm,R_(2)=10cm`
D. `R_(1)=5cm,R_(2)=5cm`

Explanation

To solve the problem of determining the largest power of a double convex lens with radii of curvature \( R_1 \) and \( R_2 \), we can follow these steps:

### Step 1: Understand the Lens Formula
The lens formula for a double convex lens is given by:
\[ \frac{1}{f} = (μ - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
Where:
- \( f \) is the focal length of the lens.
- \( μ \) is the refractive index of the lens material.
- \( R_1 \) and \( R_2 \) are the radii of curvature of the lens surfaces.

### Step 2: Determine the Sign Convention
For a double convex lens:
- \( R_1 \) is positive (convex surface).
- \( R_2 \) is negative (since it is convex from the opposite side).

Thus, the formula can be rewritten as:
\[ \frac{1}{f} = (μ - 1) \left( \frac{1}{R_1} + \frac{1}{|R_2|} \right) \]

### Step 3: Relate Focal Length to Power
The power \( P \) of the lens is given by:
\[ P = \frac{1}{f} \]
From the lens formula, we can substitute for \( \frac{1}{f} \):
\[ P = (μ - 1) \left( \frac{1}{R_1} + \frac{1}{|R_2|} \right) \]

### Step 4: Maximize the Power
To maximize the power \( P \), we need to minimize the values of \( R_1 \) and \( |R_2| \). This is because the power is inversely proportional to the radii of curvature.

### Step 5: Analyze the Given Options
If the problem provides options for \( R_1 \) and \( R_2 \), we should choose the smallest values for both \( R_1 \) and \( |R_2| \) to achieve the largest power.

### Conclusion
The largest power of the lens will occur when both \( R_1 \) and \( |R_2| \) are minimized. Therefore, if given specific values for \( R_1 \) and \( R_2 \) in the options, the option with the smallest values will yield the largest power.