# The time span for which insect can see its image?

1. The problem: A plane mirror of length 2m is kept along the line y=-x as shown in the figure. An insect having velocity of 4
cm/s is moving along x-axis from far away. The time span for which the insect can see its image will be:

A)50 sec B)25 sec C)25√2 sec D)50√2 sec

2.The answer given is D-50√2 sec

3. The Attempt at a Solution : I've tried to solve it by using laws of reflection. but i cant get the answer that is given from the options. So please help!

My solution was : the insect can see its image form the bottom of the mirror ie., for 2m for x-axis . so the time span is 2m=200 cm
time span= 200/4=50sec
but why is the answer 50√2 .
Have i done anything wrong?

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Bystander
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using laws of reflection.
How did you use the laws of reflection? Remember, the insect has to be able to see its own image.

yah to see its own image, i thought it has to be below the mirror.

Bystander
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i thought it has to be below the mirror.
Where below the mirror?

Where below the mirror?
Yah! I thought so, but i dont know for where it can see its image.

Bystander
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What's the angle of incidence for light from the insect to strike the mirror and return to the insect's eye(s)?

can you please say from where ant is able to see its own image? so that i can try the question again!

What's the angle of incidence for light from the insect to strike the mirror and return to the insect's eye(s)?
I think it should be 90 degrees so that is see its own image

Bystander
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Very good. Where on the x-axis can you arrange 90 degree incident angles with the mirror?

i did a small mistake now i get it! Thanks for the help!

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