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Two vertical plane mirrors are inclined ...

Two vertical plane mirrors are inclined at an angle of `60^@` with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other The resultant deviation is:

Text Solution

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Case I:
`delta_(1)`=clockwise deviation atA=`180^@ -2i_(1)`
`delta_(2)`anticlockwise deviation at B=`180^@-2i_(2)`
Now, from `Delta` OAB, we have
angle O + angle A + angle B = `180^@`
`implies i_(1) - i_(2) = theta`
As `i_(1)>i_(2), delta_(1)Hence, the net angle clockwise deviation=`delta_(2)`- `delta_(1)`
`=(180^@ - 2i_(2)) - (180^@ - 2i_(1))`
`=2(i_(1) - i_(2))=2theta=120^@`
Case II:
`delta_(1)`=clockwise deviation atA=`180^@ -2i_(1)`
`delta_(2)`anticlockwise deviation at B=`180^@-2i_(2)`
Now, from `Delta` OAB, we have
angle O + angle A + angle B = `180^@`
or, `theta+ (90^@-i_(1)) + (90^@ - i_(2))=180^@ implies i_(1) + i_(2)=theta`
Hence, the net angle clockwise deviation=`delta_(2) +delta_(1)`
`=(180^@-2i_(2))+(180^@-2i_(1))=360^@-2(i_(1)+i_(2))=360^@-2theta`
`implies`Net anti-clockwise deviation =`360^@ - (360^@-2theta) = 2theta=120^@`
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