Question

an object of size 5 cm is placed at a distance of 20 cm in front of a convex mirror and lens having radius of curvature 30 cm of mirror and focal and 10 cm for lens find the position of mirror formed also find the size of mirror

Answer 1

Given, Distance of the object from the convex mirror (u) = -20 cm
Radius of Curvature : 30 cm
Focal length ( f) = (30 / 2) cm
= 15 cm
Now, as we know, 1/u + 1/v = 1/f [ where f = focal length , v = distance of the image from the mirror and u = distance of the object from the mirror]
= 1/(-20) + 1/v = 1/15
= 1/v = 1/15 - (-1/20)
= 1/v = 1/15 + 1/20
= 1/v = 4 + 3 / 60 [ since. L.C.M of 15 and 20 is 60]
= 1/v = 7/60
= v = 60/7
= v = 8.5
Therefore, distance of the image from the mirror is 8.5cm.
now, Height of the object ( Ho) = 5 cm
Distance of the image from the mirror ( v) = 8.5cm
Distance of the object from the mirror ( u) = -20 cm
Since,Magnification (m) = Hi/Ho = -v/u = - 8.5 cm / -20 cm = +0.42 [ where Ho = height of the object and Hi = height of the image]
Therefore Magnification (m) = -v/u= - 8.5 cm / -20 cm = +0.42
Thus, Nature = Virtual and erect
Size = Smaller in size or diminished by the factor of 0.42
Position = 8.5 cm at the back of the mirror.