Predict/Calculate Newton's Rings Monochromatic light with

$\lambda=648 \mathrm{nm}$ shines down on a plano-convex lens lying on a piece

of plate glass, as shown in FlGURE $28-47 .$ When viewing from above,

one sees a set of concentric dark and bright fringes, referred to as

Newton's rings. (See Figure $28-13$ (b) for a photo of Newton's rings.)

(a) If the radius of the twelfh dark ring from the center is measured to

be $1.56 \mathrm{cm},$ what is the radius of curvature, $R,$ of the lens? (b) If light

with a longer wavelength is used with this system, will the radius of

the twelfth dark ring be greater than or less than 1.56 $\mathrm{cm} ?$ Explain.