Question

A point object is placed at a distance of 20 cm from a convex mirror of focal length 20 cm. The image will form at:​

Answer 1

GIVEN:

• Image distance, u = - 20 cm
• Focal length of convex mirror, f = + 20 cm

TO FIND:

Image distance, v

FORMULA:

According to mirror formula,

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

SOLUTION:

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \\ \\ \frac{1}{20} = \frac{1}{v} + \frac{1}{20} \\ \\ \frac{1}{v} = \frac{1}{20} - \frac{1}{20} \\ \\ \frac{1}{v} = \frac{1 - 1}{20} \\ \\ \frac{1}{v} = \frac{0}{20} \\ \\ \frac{1}{v} = 0 \\ \\ v = \frac{1}{0} \\ \\ v = \infty$

ANSWER:

Image distance is infinity.

Image is formed at infinite distance.

IMPORTANT POINTS:

• Focal length is positive for convex mirror and negative for concave mirror.

• All the points to the right of principal centre are positive and to the left are negative.

• All points above the principal axis are positive and below are negative.

SHORT TRICK:

• When the object is at infinity, image is formed at focus.

• When the object is at focus, image is formed at infinity.

• When the object is placed at centre, image is also formed at the centre.

• If the object is placed between infinity and center, image is formed between focus and principal centre.

• If the object is placed between focus and principal centre, the image will be formed beyond the centre.