Question

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

• A. 1 mm
• B. 0.25 mm
• C. 1.25 mm
• D. 0.5 mm

Hint:

Fringe width is directly proportional to wavelength and inversely proportional to slit separation.

Answer 1

The Correct Option is B

Step 1: Fringe width formula.
\[ \beta = \frac{\lambda D}{d} \]

Step 2: Initial fringe width.
\[ \beta = 1 \, mm \]

Step 3: New wavelength.
\[ \lambda' = \frac{\lambda}{2} \]

Step 4: New slit separation.
\[ d' = 2d \]

Step 5: Write new fringe width.
\[ \beta' = \frac{\lambda' D}{d'} \]

Step 6: Substitute.
\[ \beta' = \frac{\lambda/2}{2d} D = \frac{\lambda D}{4d} \]
\[ \beta' = \frac{\beta}{4} \]
\[ \beta' = \frac{1}{4} = 0.25 \, mm \]

Step 7: Final Answer.
\[ \boxed{0.25 \, mm} \]