At what distance from a convex lens of focal length `30cm` a object should be placed so that the size of image be`(1)/(4)`that of object?

Options

A. 30 cm
B. 60 cm
C. 150 cm
D. 90 cm

Explanation

To find the distance from a convex lens of focal length 30 cm at which an object should be placed so that the size of the image is \( \frac{1}{4} \) that of the object, we can follow these steps:

### Step 1: Understand the Magnification
The magnification \( m \) is given by the formula:
\[ m = \frac{h_i}{h_o} = \frac{V}{U} \]
where \( h_i \) is the height of the image, \( h_o \) is the height of the object, \( V \) is the image distance, and \( U \) is the object distance. Since the image size is \( \frac{1}{4} \) that of the object, we have:
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