An object 5 cm high is placed at a distance of 10cm from a convex mirror whose radius of curvature is 30 cm. Find the nature, position and size of the image.

Given mirror is convex mirror
Thus
f = R/2 = 30/2 = 15cm
u = -10cm
h = 5cm
Now we have to find the nature, position and size of image

Thus using mirror equation
1/f = 1/u + 1/v
=> 1/v = 1/f -1/u
=>1/v = 1/15+1/10
=> 1/v = 25/150
=> v = 6 cm { hence image will be formed between focus and pole .

Now magnification
m = -(v/u) = (h'/h)
m = -(-6/10)
= 3/5 { it means that the image will be virtual , erect and diminished.

Now again
m = h'/h

3/5 = h'/5
=> h' = 3cm hence the size of image will be 3cm