we are given
[tex] \frac{1}{f} =\frac{1}{d_0} +\frac{1}{d_i} [/tex]
we can solve for di
so, firstly we will isolate di
[tex] \frac{1}{f}-\frac{1}{d_0} = \frac{1}{d_i} [/tex]
[tex] \frac{1}{d_i}=\frac{1}{f}-\frac{1}{d_0} [/tex]
now, we can simplify right side by taking common denominator
[tex] \frac{1}{d_i}=\frac{d_0}{fd_0}-\frac{f}{fd_0} [/tex]
[tex] \frac{1}{d_i}=\frac{d_0-f}{fd_0} [/tex]
now, we can inverse them to find di
[tex] d_i=\frac{fd_0}{d_0-f} [/tex]...............Answer
Mirror Equations:
Concave Mirror Equation Formula :
1/f = 1/d0 + 1/di
Where, f - Focal length, di - Image distance, d0 - Object distance.
Solve:
Solution: 1/f = 1/do + 1/di ==> di = fdo/(do-f)
Solve for di: 1/f = 1/do + 1/di
Step 1: get the, 1/di by itself:
Subtract both sides by 1/do:
1/f - 1/do = 1/do + 1/di - 1/do
= 1/di = 1/f - 1/do.
Find Lowest Common Multiple (LCM.). ==> FDO
1/di = do/fdo - f / fdo
1/di = (do -f) / fdo
Answer: di = fdo / (do-f)
Therefore, Your answer would be, di = fdo / (do-f)
Hope that helps!!!! : )
