1.

Two plane mirrors are inclined at angle theta = 60^@ with each-other. A ray of light strikes one of them. Find its deviation after it has been reflected twice-one from each mirror.

Answer»

Solution :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^@`


Discussion

No Comment Found

Related InterviewSolutions