Question

Calculate the wavelength of light used in an interference experiment from the following data: Fringe width \(=0.03\) cm. Distance between the slits and eyepiece through which interference pattern is observed is 1 m. Distance between the images of the two virtual sources when a convex lens of focal length 16 cm is used at a distance of 80 cm from the eyepiece is 0.8 cm.

• A. \(0.0006\,\text{\AA}\)
• B. \(0.0006\,\text{m}\)
• C. \(6000\,\text{\AA}\)
• D. \(600\,\text{\AA}\)

Hint:

In YDSE problems: \[ \beta = \frac{\lambda D}{d} \] Lens is often used only to measure slit separation.

Answer 1

The Correct Option is C

Step 1: Fringe width: \[ \beta = \frac{\lambda D}{d} \]
Step 2: Using lens formula: \[ m = \frac{v}{u} = \frac{d'}{d} \]
Step 3: From data, slit separation: \[ d = \frac{0.8}{\frac{80}{16}} = 0.16 \text{ cm} \]
Step 4: Substitute values: \[ \lambda = \frac{\beta d}{D} = \frac{0.03 \times 0.16}{100} = 4.8\times10^{-5}\text{ cm} \]
Step 5: Convert: \[ \lambda = 6000\,\text{\AA} \]