An object is placed at 50 cm from a lens produces a virtual image at a distance of 10 cm in front of the lens . What is the focal length of the lens ? Is it converging or diverging ?

Explanation

Given
Object distance , u=-50 cm
Since the image distance is lesser than object distance and a virtual image is formed . It is a concve lens,
Image distance , v=-10 cm
To find :
Focal length of the lens, f= ?
`1/f =1/v -1/u`
`1/f =(-1)/(10) -((1)/(-50))`
`1/f =(-1)/(10)+1/(50)`
`1/f =(-50+10)/(500)`
`1/f =(-40)/(500)`
`f=(-500)/(40)`
`therefore f = -12.5` cm
It is a diverging `therefore ` it is concave lens.