Q8 of 69 Page 365

A totally reflecting, small plane mirror placed horizontally faces a parallel beam of light as shown in figure. The mass of the mirror is 20g. Assume that there is no absorption in the lens and that 30% of the light emitted by the source goes through the lens. Find the power of the source needed to support the weight of the mirror. Take g = 10 m s–2.


The weight of the mirror is supported by the light.


The weight of mirror =mg.


Force exerted on mirror is, as mirror is fully reflecting and 30% of light which is passed through the lens is used


From equation 1 of question 6 we can write



we light fall at angle θ on mirror


taking derivative of above equation and putting θ =0 as perpendicular it is falling we get



Where =power and =force ,c =speed of light.


∴ we get


Force =


∴ The force exerted by light is = .


And the power of light which is used is only 30% of original


→ for mirror to be in equilibrium the downward force and upward force must be equal.


The weight acting downwards = the force exerted by light


Weight acting downwards =Mg


Force exerted by light=


As only 30% of light is fall on mirror, therefore only 30% of the power is in use.


Force exerted by light=



Where M= mass,


g = acceleration due to gravity.


Putting the values,


20×× 10=2 .


Hence, power is ==100MW.


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