Question

An object is kept at a distance of $80cm$ in front of a plane mirror M. If the mirror is now moved $25cm$ away from the object, how does the image shift from its previous position?

Answer 1

1. The solution is:

Step 1: Given:

The initial distance of the object from the mirror is $a=80cm$

Change in the distance of the object from the mirror is $x=25cm$

Distance of object from mirror after movement is $a+x=80cm+25cm=105cm$

Step 2: Formula used:

$Dis\tan ceofobjectfrommirror=Dis\tan ceofimagefrommirror$

$a=b$

Step 3: Ray Diagram for the problem:

Ray Diagram 1: Before moving the object

Ray Diagram 2: After moving the object

Step 4: Calculation:

From above ray diagram (Diagram 2) and formula we have:

$$\begin{gathered} a=b \\ thus,a+\hspace{0.17em}x=b+y \\ 80cm+25cm=80cm+y \\ 105cm=80cm+y \\ y=105-80 \\ =25cm \\ y=25cm \end{gathered}$$

Step 5: Conclusion:

Thus, from above calculation we can say that the images moves $y=25cm$away from its original position. Hence, its distance from the mirror will be $105cm$.