A critical characteristic of light rays that are reflected diffusely from an obj

Question

A critical characteristic of light rays that are reflected diffusely from an object such as your friend's nose is the extent to which adjacent rays diverge from each other. Imagine holding a gumball 2.2 cm in diameter in front of your friend's nose as shown in the figure below. By what angle do the two tangential rays shown in the diagram diverge from each other when the center of the gumball is the following distances from the tip of your friend's nose?

Explanation / Answer

(a) tan(theta)= (1.1/7.30) because we know tan(theta)= perpendicular/ horizontal distance

Here perpendicular is taken 1.1 ,as it is the radius of the ball

So tan(theta) =0.15

Theta=tan(inverse)0.15

Angle(theta)=8.53degree

And 2(theta)=17.06 this is the angle by which two rays diverse if d=7.30cm

(b)tan (theta)=1.1/29.2=0.038

Theta=2.17

And 2(theta)=4.34 degree if d=29.2cm

(c)=tan(theta)= 1.1/146 =0.0075

Theta=0.00013 degree

So 2(theta)=0.00026 degree If d=146cm

(d)tan(theta)=1.1/1.46*10to the power7

Because 146km=1.46*10 to the power 7

Here theta comes zero that means if d is very large I.e. 146km.the two rays don't diverge , they are equivalent to one ray.

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