Question

An object is placed 15cm from a convex mirror of radius of curvature 90cm. Calculate image position and magnification.

Answer 1

Step 1: Given

Radius of curvature(R)= 90 cm

Object distance(u)= -15 cm (in front of mirror)

Focal length(f)= R/2= 90/2 = 45 cm

Step 2: Formula used

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$ (mirror formula)

Magnification(m) = $-\frac{v}{u}$

Step 3: Finding the image distance

$\frac{1}{45}=\frac{1}{-15}+\frac{1}{v}$

$\frac{1}{v}=\frac{4}{45}$

v=45/4 cm

Hence, image distance(v)= 45/4 cm = 11.25 cm

Step 4: Finding the magnification

Magnification(m)= $-\frac{v}{u}$ =$-\frac{11.25}{-15}$ = o.75

Hence, the magnification is 0.75 and the image distance is 11.25 cm.