(a) Calculation of distance of an object and location of image
(b) Reason for virtual image, through convex mirror
(a) Given R=−20‌cm , and magnification m=−2
Focal length of the mirror f=‌

R

2

=−10‌cm
‌⇒‌‌−‌

1

10

=‌

1

2u

+‌

1

u

‌⇒‌‌u=−15‌cm
‌∴‌‌v=2×−15‌cm=−30‌cm
‌‌ Magnification ‌(m)=−‌

v

u

‌−2=−‌

v

u

‌⇒‌‌v=2u
Using mirror formula
‌

1

f

=‌

1

v

+‌

1

u

(b) ‌

1

f

=‌

1

v

+‌

1

u

Using sign convention, for convex mirror, we have
f>0,u<0
From the formula
‌

1

v

=‌

1

f

−‌

1

u

∵f is positive and u is negative,
⇒v is always positive, hence image is always virtual.