In a YDSE , D= 1m , d =1mm and wavelength= ½ mm .

1. find the distance between the first and central maxima on the screen .

1. Find the no of maxima and minima obtained on the screen

Please eexplain in detail

To solve the problem of finding the distance between the first and central maxima in a Young's Double Slit Experiment (YDSE), as well as the number of maxima and minima on the screen, we can use some fundamental principles of wave optics. Let's break this down step by step.

Understanding the Setup

In a YDSE, two coherent light sources emit waves that interfere with each other. The distance between the slits is denoted as d, the distance from the slits to the screen is D, and the wavelength of the light used is represented by λ.

Given Values

• Distance from slits to screen (D) = 1 m
• Distance between the slits (d) = 1 mm = 0.001 m
• Wavelength (λ) = ½ mm = 0.0005 m

Calculating the Distance Between Maxima

The position of the maxima on the screen can be calculated using the formula:

y = (m * λ * D) / d

where y is the distance from the central maximum, m is the order of the maximum (0 for central, 1 for first order, etc.), λ is the wavelength, D is the distance to the screen, and d is the distance between the slits.

Finding the Position of the First Maximum

For the first maximum (m = 1):

y₁ = (1 * 0.0005 m * 1 m) / 0.001 m

y₁ = 0.5 m

The distance between the central maximum (m = 0) and the first maximum (m = 1) is therefore:

Distance = y₁ - y₀ = 0.5 m - 0 = 0.5 m

Determining the Number of Maxima and Minima

The total number of maxima and minima can be determined by considering the maximum possible order of maxima that can fit on the screen. The maximum order m can be calculated using the condition:

m * λ ≤ d

Rearranging gives:

m ≤ d / λ

Calculating Maximum Order

Substituting the values:

m ≤ 0.001 m / 0.0005 m = 2

This means we can have maxima for m = 0, 1, and 2, which gives us a total of 3 maxima.

Counting Minima

For every maximum, there is a minimum in between. Therefore, the number of minima will be one less than the number of maxima. Since we have 3 maxima, we will have:

Number of minima = Number of maxima - 1 = 3 - 1 = 2

Summary of Results

• Distance between the first and central maxima: 0.5 m
• Total number of maxima: 3
• Total number of minima: 2

This analysis shows how wave interference leads to distinct patterns of light and dark on the screen, illustrating the principles of wave optics effectively. If you have any further questions or need clarification on any part, feel free to ask!