An object of height 5 cm is placed at a distance of 10 cm from convex mirror of focal length 15 cm. Find the position, nature and size of an image.

Sure, I can help with that. To find the position, nature, and size of the image, we can use the mirror formula and magnification formula.

The mirror formula is 1/v + 1/u = 1/f, where:

• v is the image distance
• u is the object distance
• f is the focal length

Given that the object is placed at a distance of 10 cm from the mirror, u = -10 cm (the negative sign indicates that the object is on the same side of the mirror as the light source). The focal length of the convex mirror is given as 15 cm, so f = -15 cm (the focal length is negative for a convex mirror).

Substituting these values into the mirror formula gives us:

1/v - 1/10 = -1/15

Solving this equation for v gives us v = -30 cm. The negative sign indicates that the image is formed on the same side as the light source.

The magnification (m) of the mirror is given by the ratio of the height of the image (h') to the height of the object (h), and is also equal to -v/u. Therefore, we can write:

m = h'/h = -v/u

Substituting the given object height (h = 5 cm) and the calculated image distance (v = -30 cm) into this equation gives us:

h' = m * h = (-(-30)/-10) * 5 = -15 cm

The negative sign indicates that the image is inverted.

So, the image is located 30 cm from the mirror on the same side as the light source, it is inverted, and it is 15 cm tall.