Question

In YDSE, how many maximas can be obtained on a screen, including central maxima, on both sides of the central fringe if \( \lambda = 3000\) Å, \( d = 5000\) Å?

• A. 2
• B. 5
• C. 3
• D. 1

Hint:

For Young’s double-slit experiment:
- The condition for maximas is \( d \sin \theta = m \lambda \).
- The number of maximas depends on the ratio \( d/\lambda \).

Answer 1

The Correct Option is C

To determine the total number of maximas in Young’s Double-Slit Experiment (YDSE), we use the condition for interference maximas.
Step 1: Given Data
- Wavelength of light: \( \lambda = 3000 \) Å \( = 3 \times 10^{-7} \) m
- Slit separation: \( d = 5000 \) Å \( = 5 \times 10^{-7} \) m
Step 2: Condition for Maxima
The condition for maximas in YDSE is given by the equation:
\[ d \sin \theta = m \lambda \] where \( m \) is the order of the maxima, and \( \theta \) is the angle at which the maxima occurs. The maximum order of maxima is obtained when \( \sin \theta = 1 \), i.e., at the extreme possible angle. Thus,
\[ m_{{max}} = \frac{d}{\lambda} \] Step 3: Calculate Maximum Order of Maxima
\[ m_{{max}} = \frac{5 \times 10^{-7}}{3 \times 10^{-7}} \] \[ m_{{max}} = \frac{5}{3} \approx 1.67 \] Since \( m \) must be an integer, we take the largest integer \( m_{{max}} = 1 \).
Step 4: Counting Total Maximas
- Maximas exist for \( m = 0 \) (central maxima) and \( m = \pm1 \) (on both sides).
- This gives a total of \( 3 \) maximas: one central and one on each side.
Thus, the correct answer is:
\[ {3} \]