Question

1.) In a double-slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0 cm. What happens to the distance between adjacent maxima when the slit separation is doubled?

A.) It decreases to 0.5 cm.

B.) It increases to 4.0 cm.

C.) It increases to 2.0 cm.

D.) It decreases to 0.25 cm.

E.) It remains the same.

2.) In a two-slit experiment, monochromatic coherent light of wavelength 500 nm passes through a pair of slits separated by 1.30 x 10^-5 m. At what angle away from the centerline does the first bright fringe occur?

A.) 1.56°

B.) 2.20°

C.) 3.85°

D.) 2.73°

E.) 4.40°

3.) In a two-slit experiment, the slit separation is 6.50 × 10^-5 m. The interference pattern is created on a screen that is 1.60 m away from the slits. If the 6th bright fringe on the screen is 8.00 cm away from the central fringe, what is the wavelength of the light?

A.) 138 nm

B.) 204 nm

C.) 271 nm

D.) 417 nm

E.) 542 nm

Answer 1

1)
given the distance between adjacent maxima on a remote screen is y1 = 1.0 cm

let the separation between the slits is d1.

if the separation between the slits is double that is d2 = 2d1

then y2 =?

we know the relation is y = m*lambda *D/d
where D is separation of slits and screen here it is constant , and wavelength lambda also
  

   so y2/y1 = d1/d2

   y2 = d1*y1/d2

   y2 = d1*y1/2*d1

   y2 = y1/2

means y2 = 1.0/2 cm = 0.5 cm

answer is opiton A) It decreases to 0.5 cm.

2)

condition for the bright fringe is

   d sin theta = m*lambda
  
   sin theta = m*lambda/d

for cnetral fringe

   sin theta = 1*lambda/d

   theta = arc sin (lambda/d)

   theta = arc sin ((500*10^-9)/(1.30*10^-5)) degrees

   theta = 2.20 degrees

answer is option B

3)

slit separation d = 6.50*10^-5 m

D = 1.60 m

m= 6

y6 = 8.00 cm

we know that the mth bright fringe distance from the central bright fringe is

   ym = m*lambda*D/d

   lambda = ym*d/(m*D)

here m = 6

   lambda = (y6*d)/(m*D)

   lambda = (0.08*6.50*10^-5)/(6*1.6) m

   lambda = 5.4166666666667*10^-7 m
  
   lambda = 541.66 nm = 542 nm

Answer is option E 542 nm