Question

A concave mirror of focal length 10cm is placed at a distance of 35cm from a wall. How far from the wall should an object be placed so that its real image is formed on the wall?

Answer 1

Hint: In order to solve the above question first we will check what all quantities are given to us and what we have to find. Here, we will use mirror formula to find the distance from the wall at which the object should be placed because focal length and distance of object is given above

Complete step-by-step solution:
In the above question let us check what quantities are given to us:
Focal length of the mirror is 10 cm
Distance of the object from the wall is 35 cm
Now, we want to get the real image of the object on the wall. That means the distance of the image is 35cm only.
So, to solve this question we will use the mirror formula which is as follows:
\[\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}\]
Where f is the focal length,
u is the distance of the given object
v is the distance of the image from the screen
Here, in the given question the value of focal length that is f is -10 cm and the value of distance of image from the screen that is v is -35 cm.
applying all these values in the mirror formula we will get:
\[=\dfrac{1}{-10}+\dfrac{1}{35}=\dfrac{1}{u}\]
\[\begin{align}
  & =\dfrac{-7+2}{70} \\
 & =\dfrac{-5}{70} \\
 & =\dfrac{-1}{14} \\
\end{align}\]
we get the value of u that is the distance of the object as -14 cm which means it should be placed 14 cm away from the mirror.
But this is the not answer we want we have to find the distance of the object from the wall not from the mirror and we know that the distance of the wall from the mirror is 35 cm
So, we will subtract the distance of the mirror from the object from the distance of the wall from the mirror:
This means,
Distance of object from the wall\[=35-14\]
Distance of object from the wall \[=21cm\]
So, the distance of the object from the wall is 21 cm to get a real image on the wall.

Note:Here, in the above question we have to find the distance of the object from the wall not the distance of the object from the mirror. So. Remember this that here the answer will not be 14 am we have to subtract the distance of wall from the mirror from the distance of object from the mirror.