The correct option is
A 10 cm
The approach that we follow in the given situation is to get the image of a 2-D object is to locate the image of the two extreme points and finally join these images of two extreme points to get the full image of the 2-D object.
From the diagram we see that we can take two extended object and apply mirror formula for them.
Let's name them AB & CD.
First of all for AB,
u = − 30cm, f = − 10cm
We get, by applying mirror formula,
1v+1u=1f
Or,
1v=1f−1u
=−110−−130
=−15 cm
So the image is at a distance 15cm from the mirror on the left side.
Now let's find the size of this image.
We have the magnification formula
hiho=−vu=−1530=−12.
a negative sign indicates here that the image is inverted
Or,
hi=−12×10 cm=−5 cm
Or, the magnitude of the height is 5 cm.
Now, the same process we will repeat for our second extended object CD.
We have,
u = − 40 cm, f = − 10 cm
We get by applying mirror formula,
1v+1u=1f
Or,
1v=1f−1u
=−110−−140
v=−403 cm
So the image is at a distance
403 cm from the mirror.
Now, for the size of the image, we will use the magnification formula
hiho=−vu=403×−110=−13
a negative sign indicates here that the image is inverted
Or,
hi=−13×10 cm=−103 cm
Or, the magnitude of the height is
103 cm.
So, finally the image looks like this:
We see that the total length of the image is
53 cm+5cm+103 cm=10 cm.