Irina finds an unlabeled box of fine needles, and wants to determine how thick they are. a standard ruler will not do the job, as each needle is less than a millimeter thick. so, to find the thickness, she uses a needle to poke a hole in a piece of brown construction paper. then, she positions a 640 nm laser pointer to shine through the hole and project a circular diffraction pattern on a wall 21.7 m away. she then uses her ruler to measure that the central bright circle is 14.2 cm in diameter. what diameter does irina calculate for the needle?

Explanation:

The expression which represent the first diffraction minima by a circular aperture is given by --------eqn 1

The angle through which the first minima is diffracted is given by ---------eqn 2

As is very small so we can write

So from eqn 1 and eqn 2 we can write

--------eqn 3

Here is the position of first maxima D is the distance of screen from the circular aperture d is the diameter of aperture

It is given that diameter of circular aperture is 14.7 cm so

Now putting all these value in eqn 3

option number c is the right answer.

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form