A object is placed 20 cm from the convex lens, with focal length 40 cm. The image formed is virtual and erect.
What will be power of the lens?

Options

A. `-2.5D`
B. `+0.025D`
C. `+2.5D`
D. `-0.025D`

Explanation

To solve the problem step by step, we will use the lens formula and the formula for the power of a lens.

### Step 1: Identify the given values
- Object distance (u) = -20 cm (negative because the object is on the same side as the incoming light)
- Focal length (f) = +40 cm (positive for a convex lens)

### Step 2: Use the lens formula
The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
Rearranging this gives:
\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]

### Step 3: Substitute the values into the lens formula
Substituting the values of f and u into the formula:
\[ \frac{1}{v} = \frac{1}{40} + \frac{1}{-20} \]

### Step 4: Calculate the right side
Calculating the right side:
\[ \frac{1}{v} = \frac{1}{40} - \frac{1}{20} \]
To combine these fractions, find a common denominator (which is 40):
\[ \frac{1}{v} = \frac{1}{40} - \frac{2}{40} = \frac{-1}{40} \]

### Step 5: Solve for v
Taking the reciprocal gives:
\[ v = -40 \text{ cm} \]
The negative sign indicates that the image is virtual and located on the same side as the object.

### Step 6: Calculate the power of the lens
The power (P) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
Where f is in meters. First, convert the focal length from centimeters to meters:
\[ f = 40 \text{ cm} = 0.4 \text{ m} \]
Now substitute into the power formula:
\[ P = \frac{1}{0.4} = 2.5 \text{ diopters} \]

### Step 7: Convert to centimeters
If we want to express the power in terms of centimeters:
\[ P = \frac{100}{f} \text{ (for f in cm)} \]
So,
\[ P = \frac{100}{40} = 2.5 \text{ diopters} \]

### Final Answer
The power of the lens is \( +2.5 \text{ diopters} \).

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