Question

1) A plano-convex lens having a radius of curvature of r = 2.20 m is placed on a concave glass surface whose radius of curvature is R = 13.0 m as shown in the figure below. Assuming 515-nm light is incident normal to the flat surface of the lens, determine the radius of the 100th bright ring.
cm
2)
Light of wavelength 589.0 nm illuminates a slit of width 0.80 mm.
(a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.87 mm from the central maximum?
m

(b) Calculate the width of the central maximum.
mm

Answer 1

(1) Write the formula for Newton's rings

Rm = sqrt[(m+½) λR]

where -

m is mth ring (here m = 100)
Rm is radius of the mth Newton's bright ring
λ is the wavelength of the light passing through (515 nm = 515x10^-9 m)
R is the radius of curvature of the plano-convex lens the light is passing through (2.20 m)

put these values in the above expression -

Rm = sqrt[(100+½) 515x10^-9x2.2] = 0.01067 m = 1.067 cm

(2) (a) Apply the formula -

d*sinΘ = mλ

now, sinΘ=Y/L

So, dY/L = λ

=> L = dY/λ

=> L= (8.0 * 10^-4)(.00087)/(589 * 10^-9)
=> L= 1.182 m

(b) Width of the central maximum = 0.87 x 2 = 1.74 mm