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Question

A U-shaped wire is placed before a concave mirror having radius of curvature 20 cm as shown in figure. Find the total length of wire in the image.




A
10 cm
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B
20 cm
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C
30 cm
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D
5 cm
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Solution

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=1f1u

=110130

=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=1f1u

=110140

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.

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