Q.8. A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

Step 1: Identify the given values

The object distance (u) is -12 cm (negative because it is on the same side as the light being reflected). The focal length (f) of the convex mirror is -15 cm (negative because it is a convex mirror).

Step 2: Use the mirror formula to find the image distance (v)

The mirror formula is 1/f = 1/v + 1/u. We can rearrange this to find v: 1/v = 1/f - 1/u.

Substituting the given values:

1/v = 1/(-15) - 1/(-12) 1/v = -1/15 + 1/12 1/v = -4/180 + 15/180 1/v = 11/180

So, v = 180/11 = 16.36 cm

The image distance is positive, which means the image is formed on the same side as the light being reflected.

Step 3: Use the magnification formula to find the magnification (m)

The magnification formula is m = -v/u.

Substituting the given values:

m = -16.36 / -12 = 1.36

The magnification is positive, which means the image is upright. The magnitude of the magnification is greater than 1, which means the image is magnified.

Step 4: Describe what happens as the needle is moved farther from the mirror

As the needle is moved farther from the mirror, the object distance (u) increases. According to the mirror formula, as u increases, v (the image distance) also increases. This means the image moves farther away from the mirror.

Also, as u increases, the magnification (m) decreases (since m = -v/u). This means the image becomes smaller. So, as the needle is moved farther from the mirror, the image becomes smaller and moves farther away from the mirror.