Question

a convex lens produces an image of an object on a screen with the magnification of half when the lens is moved towards 30cm away from the object the magnification of the images 2. what is the focal length of the lens

Answer 1

Answer:

20 cm

Explanation:

We know that  

m=  f−v

​ As given, 2 1 = f

f−v

​f=2(f−v)

f=2f−2v

2v=2f−f

2v=f

v=(2 f )→(i)

Now we havem=2

and  v  1

=(v+30)

⇒m=  f

f−v

​Right arrow 2=  f

f−(v+30)

⇒2=  f

f−(f/2+30)

(from(i))

2f=f−f/2+30

⇒2f=  

2 f +30

⇒2f−  2f =30cm

⇒  2

4f−f

​=30cm =2 =3f

=30 ⇒3f=60

⇒f=20cm