Question

A convex lens has a focal length of 10 cm. At what distance from the lens should the object be placed so that it forms a real and inverted image 20 cm away from the lens? What would be the size of the image formed if the object is 2 cm high? With the help of a ray diagram show the formation of the image by the lens in this case.

Answer 1

According to the question; 

Object distance = u; 

Image distance (v) = 20cm;

Focal length = 10cm 

By lens formula;

\(\frac1v-\frac1u=\frac1f\)

⇒ \(\frac1{20}-\frac1u=\frac1{10}\)

⇒ \(\frac1{u}=\frac1{20}-\frac1{10}\)

⇒ \(\frac1{u}=\frac{1-2}{20}-\frac{-1}{20}\)

⇒ \(\frac1{u}=\frac{-1}{10}\)

⇒ u = -20cm. 

Therefore, object is placed at 20 cm in front of lens. 

Now;

Height of object h₁= 2cm;

Magnification = \(\frac{h_2}{h_1}=\frac{v}u\)

Putting values of v and u

Magnification = \(\frac{h_2}{2}=\frac{20}{-20}\)

⇒ \(\frac{h_2}{h_1}= -1;\)

⇒ h₂ = 2 x -1 = -2

Height of image is 2 cm. 

Negative sign means image is inverted. 

Thus, the image is real, inverted and same as size of object. 

Diagram below shows the image formation.