Question

An object is placed at a distance of 30 cm in front of a convex lens of focal length 15 cm. Use lens formula to determine the position of the image. What will be the size of the image in this case?

Hint:

Object at 2f of convex lens → Image at 2f, same size, inverted.

Answer 1

Given:

Object distance (u) = −30 cm
Focal length of convex lens (f) = +15 cm

(Using sign convention: For a convex lens, f is positive and object distance u is negative.)

Step 1: Use Lens Formula

Lens formula:
1/f = 1/v − 1/u

Substitute the values:

1/15 = 1/v − 1/(−30)

1/15 = 1/v + 1/30

Take LCM of 30:

1/15 = 2/30

So,

2/30 = 1/v + 1/30

2/30 − 1/30 = 1/v

1/30 = 1/v

Therefore,

v = +30 cm

Step 2: Nature and Position of Image

Since v is positive, the image is formed 30 cm on the other side of the lens.
The image is real and inverted.

Step 3: Find Magnification (Size of Image)

Magnification (m) = v/u

m = 30 / (−30) = −1

Magnification = −1

This means:
– Image is inverted (negative sign).
– Image is of the same size as the object (|m| = 1).

Conclusion:
The image is formed at 30 cm on the other side of the convex lens. It is real, inverted, and of the same size as the object.