Answer:
u = - 20 cm
m =[tex]\frac{1}{5}[/tex]
Given:
Radius of curvature, R = 10 cm
image distance, v = 4 cm
Solution:
Focal length of the convex mirror, f:
f = [tex]\frac{R}{2} = \frac{10}{2} = 5 cm[/tex]
Using Lens' maker formula:
[tex]\frac{1}{f} = \frac{1}{u} + \frac{1}{v}[/tex]
Substitute the given values in the above formula:
[tex]\frac{1}{5} = \frac{1}{u} + \frac{1}{4}[/tex]
[tex]\frac{1}{u} = \frac{1}{5} - \frac{1}{4}[/tex]
u = - 20 cm
where
u = object distance
Now, magnification is the ratio of image distance to the object distance:
magnification, m =[tex]\frac{|v|}{|u|}[/tex]
magnification, m =[tex]\frac{|4|}{|-20|}[/tex]
m =[tex]\frac{4}{20}[/tex]
m =[tex]\frac{1}{5}[/tex]
