1.

A ray of light is incident at 50^(@) on the middle of one of the two mirros arranged at an angle of 60^(@) between them. The ray then touches the second mirror, making an angle of incidence of

Answer»

`50^(@)`
`60^(@)`
`70^(@)`
`80^(@)`

Solution :(c ) LET required angle be `THETA`

From geometry of FIGURE
In `Delta ABC , alpha = 180^(@) - (60^(@) + 40^(@)) = 80^(@)`
`rArr beta = 90^(@) - 80^(@) = 10^(@)`
In `Delta ABD , angle A = 60^(@), angle B = (alpha = 2 beta)`
`=(80 + 2 xx 10) = 100^(@) and angle D = (90^(@) - theta)`
`therefore angleA + angle B + angle D = 180^(@) rArr 60^(@) + 100^(@) + (90^(@) - theta)`
` = 180^(@) rArr theta = 70^(@)`.


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