Question

An object placed 45 cm from a lens forms an image on a screen place 90 cm on the other side of the lens. Identify the type of the lens and find its focal length.

Answer 1

According to the question; 

Object distance, u= -45cm; 

Image distance, v= 90 cm; 

Focal length, f=? 

By lens formula; 

\(\frac{1}{v}\,-\,\frac1u\,=\,\frac1f\)

⇒ \(\frac{1}{90}\,-\,\frac{1}{-45}\,=\,\frac1f\)

⇒\(\frac{1}{f}\,=\,\frac1{90}\,+\,\frac1{45}\)

⇒\(\frac{1}{f}\,=\,\frac{1+2}{90}\,=\,\frac{3}{90}\)

⇒ f =\(\frac{90}3\)

= f = 30cm.

Since the focal length is positive, therefore the lens is convex lens of focal length 30cm.