Question 23: Wave Optics

Question

In the Young's double slit experiment, when a monochromatic light is used, fringe width obtained is 1 mm . If the wave length is halved and the slit width is doubled, what will be the new fringe width?

Accepted Answer

We know in YoungÃ¢ÂÂs doubleÃ¢ÂÂslit experiment the fringe width is given by
$$\beta = \frac{D\,\lambda}{d}$$
where
Ã¢ÂÂ¢ D = distance screenÃ¢ÂÂslits (fixed)
Ã¢ÂÂ¢ ÃÂ» = wavelength of light
Ã¢ÂÂ¢ d = slit separation
Originally,
$$\beta_0 = 1	ext{ mm} = \frac{D\,\lambda}{d}\,. $$
Now ÃÂ» is halved (ÃÂ»Ã¢ÂÂÃÂ»/2) and the slit separation is doubled (dÃ¢ÂÂ2d).  Hence
$$\beta'  = \frac{D\,(\lambda/2)}{2d}  = \frac{D\,\lambda}{4\,d}  = \frac{\beta_0}{4}  = \frac{1	ext{ mm}}{4}  = 0.25	ext{ mm}. $$
Answer: 0.25 mm (Option B).

Answer

1 mm

Answer

0.25 mm

Answer

1.25 mm

Answer

0.5 mm

Wave Optics

In the Young's double slit experiment, when a monochromatic light is used, fringe width obtained is 1 mm . If the wave length is halved and the slit width is doubled, what will be the new fringe width?

Choose the correct answer: