A teacher sets up the stand carrying a convex lens of focal length 15 cm at 42.7 cm mark on the optical bench. He asks four students A, B, C and D to suggest the position of screen on the optical bench so that a distinct image of a distant tree is obtained almost immediately on it. The positions suggested by the students were as :
(i) 12.7 cm
(ii) 29.7 cm
(iii) 57.7 cm
(iv) 72.7 cm
The correct position of the screen was suggested by

Options

A. (i)
B. (ii)
C. (iii)
D. (iv)

Explanation

To find the correct position of the screen on the optical bench for obtaining a distinct image of a distant tree using a convex lens, follow these steps:

### Step 1: Understand the setup
A convex lens is used to form an image of a distant object (in this case, a tree). The focal length of the lens is given as 15 cm. The lens is positioned at the 42.7 cm mark on the optical bench.

### Step 2: Identify the formula for image formation
For a distant object, the image is formed at a distance from the lens equal to the focal length added to the position of the lens. The formula can be expressed as:
\[ \text{Position of the screen} = \text{Position of the lens} + \text{Focal length} \]

### Step 3: Substitute the values
Substituting the known values into the formula:
- Position of the lens = 42.7 cm
- Focal length (F) = 15 cm

Now, calculate the position of the screen:
\[ \text{Position of the screen} = 42.7 \, \text{cm} + 15 \, \text{cm} \]
\[ \text{Position of the screen} = 57.7 \, \text{cm} \]

### Step 4: Conclusion
The correct position of the screen to obtain a distinct image of the distant tree is at 57.7 cm. Therefore, the correct suggestion was made by student C.