A point object is kept 60 cm in front of a spherical convex surface . . .

Question : A point object is kept 60 cm in front of a spherical convex surface (n=1.5) Radius of curvature 40 cm. The image formed is 
(A) real, at a distance 1.8 m from the surface
(B) virtual, at a distance 1.8 m from the surface. 
(C) real, at a distance 3.6 m from the surface. 
(D) virtual, at a distance 3.6 m from the surface. 

Doubt by Gurdev

Solution : 
u=-60 cm 
R = +40 cm 
n1= 1 (air) 
n2=1.5

Using 
n2/v-n1/u=(n2-n1)/R
1.5/v-1/(-60)=(1.5-1)/40
1.5/v+1/60=0.5/40
1.5/v=0.5/40-1/60
1.5/v=5/400-1/60
1.5/v=1/80-1/60
1.5/v=60-80/(80×60)
1.5/v=-20/(80×60)
15/10v=-20/4800
15/10v=-20/4800
15/v=-1/24
v/15=-24
v=-24×15
v=-360
v=-3.6 m 

-ve sign shows that the image is on the same side as the object i.e image is virtual. 

Hence, (D) virtual, at a distance 3.6 m from the surface is the correct option.