Question
How far apart are an object and an image formed by a 75.0cm focal length converging lens if the
image is 2.5x larger than the object and is real.
Please, help me.
image is 2.5x larger than the object and is real.
Please, help me.
Answers
Amir
Use two equations to get di and do. First, 1/f=1/do+1/di (textbooks usually use p and q).
Also, M = -di/do.
Since the image is real, di is positive and M is negative (image is upside down). Using the second equation, -2.5 = -di/do. Solving for di, di=2.5*do.
We can substitute this into first equation to get, 1/75 = 1/do + 1/(2.5*do). Solving for do, do = 105.
Now we put this into either equation, for example, 1/75 = 1/105 + 1/di and solve for di: di = 262.5
So finally, di + do = 105 + 262.5 = 367.5 cm
Also, M = -di/do.
Since the image is real, di is positive and M is negative (image is upside down). Using the second equation, -2.5 = -di/do. Solving for di, di=2.5*do.
We can substitute this into first equation to get, 1/75 = 1/do + 1/(2.5*do). Solving for do, do = 105.
Now we put this into either equation, for example, 1/75 = 1/105 + 1/di and solve for di: di = 262.5
So finally, di + do = 105 + 262.5 = 367.5 cm