Fig. 6.1 shows wavefronts incident on, and emerging from, a double slit arrangement.

Question 19

Fig. 6.1 shows wavefronts incident on, and emerging from, a double slit arrangement.

Fig. 6.1

The wavefronts represent successive crests of the wave. The line OX shows one direction along which constructive interference may be observed.

(a) State the principle of superposition. [3]

(b) On Fig. 6.1, draw lines to show

(i) a second direction along which constructive interference may be observed (label

this line CC),

(ii) a direction along which destructive interference may be observed (label this line

DD). [2]

(c) Light of wavelength 650 nm is incident normally on a double slit arrangement. The

interference fringes formed are viewed on a screen placed parallel to and 1.2 m from the

plane of the double slit, as shown in Fig. 6.2.

Fig. 6.2

The fringe separation is 0.70 mm.

(i) Calculate the separation a of the slits. [3]

(ii) The width of both slits is increased without changing their separation a. State the

effect, if any, that this change has on

1. the separation of the fringes,

2. the brightness of the light fringes,

3. the brightness of the dark fringes.

[3]

Reference: Past Exam Paper – June 2004 Paper 2 Q6

Solution:

(a) The principle of superposition states that when two (or more) waves meet,

the resultant displacement is the (vector) sum of the individual displacements at that point.

(b)

(i) Any correct line passing through the points of intersection of crests

  

(ii)

Any correct line through the intersections of a crest and a through

{a line midway between any 2 CC lines.}

(c)

(i)

{For a double slit,}

λ = ax / D

650×10^-9 = (a × 0.70×10^-3) / 1.2

Separation, a = 1.1×10^-3 m

(ii)

1. No change                                                  

2. Brighter

3. No change (accept stay/remain dark)

{Dark fringes are formed when light from the slits superpose and cancel each other out completely giving no (zero) resultant displacement. We cannot get a resultant displacement less than zero. So, the dark fringes remain dark.}