Question

Please help and explain I have no idea this was supposed to be math

Answer 1

Remember that the thin-lens equation relates the fcal length (f) of a tin lens with the distance from the lens to the ojbject d_o and the distance from the lens to the image, d_o.

According to he txext of the image, the focal length is equal to x cm and the distance from the lens to the object is x+20cm. Then, f and d_o are known and we are asked to find an expression fo d_i. Isolate d_i from the equation:

`\begin{gathered} (1)/(f)=(1)/(d_i)+(1)/(d_o) \\ \\ \Rightarrow(1)/(d_i)=(1)/(f)-(1)/(d_o) \\ \\ \Rightarrow(1)/(d_i)=(d_o-f)/(fd_o) \\ \\ \Rightarrow d_i=(fd_o)/(d_o-f) \end{gathered}`

Replace f=x and d_o+x+20:

`d_i=((x)(x+20))/((x+20)-x)=(x(x+20))/(x+20-x)=(x(x+20))/(20)=(1)/(20)x^2+x`

The distance from the lens to the place where the image is form is given by the expression x(x+20)/20.

Therefore,the expression in simplest oform for how far from the lens should a screen be placed to put the image in focus, is:

`(1)/(20)x^2+x`