An object and a screen are kept at a distance of 120 cm A lens of focal length `22.5` cm is kept between them so that a real image is formed on the screen Find the possible location (s) of the lens.

Options

A. 90cm from object
B. 30cm from object
C. 40cm from object
D. 80cm from object

Answer

A, B

Explanation

`1/f=1/v-1/u`
`1/(22.5)=1/y-1/(-x)=1/x+1/y=(x+y)/(xy)`
`x+y=120 xy=120xx22.5`
`x(120-x)=120xx22.5`
`x^(2)-120x+120xx22.5=0`
`x=(120pmsqrt(120^(2)-4xx120xx22.5))/(2)`
`=(120pmsqrt(120^(2)-120xx90))/2`
`=(120pm10sqrt(36))/2=60 pm 30 ,`x=30 or 90`