The real image which is exactly equal to the size of an object is to be obtained on a screen with the help of a convex glass of focal length 15 cm. For this, what must be in the distance between the object and the screen?

Options

A. 15 cm
B. 30 cm
C. 45 cm
D. 60 cm

Explanation

To solve the problem, we need to find the distance between the object and the screen when a real image is formed that is equal in size to the object using a convex lens with a focal length of 15 cm.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Focal length of the lens (F) = 15 cm
- The image is real and of the same size as the object.

2. **Understanding Magnification:**
- The magnification (M) is defined as the ratio of the height of the image (h') to the height of the object (h):
\[ M = \frac{h'}{h} \]
- Since the image is of the same size as the object, we have:
\[ M = 1 \]

3. **Relate Magnification to Object and Image Distance:**
- Magnification can also be expressed in terms of object distance (U) and image distance (V):
\[ M = \frac{V}{U} \]
- Since \( M = 1 \), we can write:
\[ \frac{V}{U} = 1 \implies V = U \]

4. **Using the Lens Formula:**
- The lens formula is given by:
\[ \frac{1}{F} = \frac{1}{V} - \frac{1}{U} \]
- Substituting \( V = U \) into the lens formula, we get:
\[ \frac{1}{15} = \frac{1}{U} - \frac{1}{U} \implies \frac{1}{15} = \frac{1}{U} - \frac{1}{(-U)} \]
- This simplifies to:
\[ \frac{1}{15} = \frac{1}{U} + \frac{1}{U} = \frac{2}{U} \]

5. **Solving for U:**
- Rearranging the equation gives:
\[ U = 2 \times 15 = 30 \text{ cm} \]

6. **Finding the Distance Between Object and Screen:**
- Since \( V = U \), the distance between the object and the screen (which is the sum of the object distance and the image distance) is:
\[ \text{Distance} = U + V = 30 \text{ cm} + 30 \text{ cm} = 60 \text{ cm} \]

### Final Answer:
The distance between the object and the screen is **60 cm**.