Question

the image of an object formed by a lens is of magnification -1 if the distance between the object and the image is 60 cm what is the focal length of the lens if the object is moved 20 cm towards lens where should the image be formed state reasons and also draw Ray diagrams

Answer 1

The magnification of the object and image= -1

The distance between the object and image is 60 cm

Let the distance of the object be x cm

so the distance of the image be (60-x)cm

Now the object moved 20 cm towards the lens,

Distance of the object become ,u=-(x-20)cm

Distance of the image,v= (60-×+20) cm=(80-x)cm

As we know,

m= v/u

-1= (80-x)/-(x-20)

x-20=80-x

x+x=80+20

2x=100

x=50 cm

Now u=- (x-20)

u= -(50-20)

u = -30 cm

v= 80 -×

v = 80-50

v= 30 cm

lens formula ,

1/f =1/v-1/u

1/f=1/30+1/30

1/f=(1+1)/30

f =15 cm