A two-slit pattern is viewed on a screen 1.17 m from the slits. What is the width of the central bright fringe, if the third dark fringes on either side are 26.4 cm apart?

The coordinate of dark fringe is

y=(2k+1)Lλ/2d.

The width of the central bright fringe= the distance between the first dark fringes is
2y₁=2•(2•1+1)Lλ/2d =3 Lλ/d.
The distance between the third dark fringes is
2y₃=2•(2•3+1)Lλ/2d=7 Lλ/d.
2y₁/2y₃=(3 Lλ/d)/( 7 Lλ/d),
2y₁/2y₃=3/7,
2y₁=2y₃•3/7=
=26.4•3/7=11.3 cm

Sorry not the right answer

To find the width of the central bright fringe, we need to consider the pattern created by the two slits. This pattern is known as an interference pattern.

In this case, the width of the central bright fringe can be determined using the formula for the fringe separation, which is given by:

λ = (d * L) / w

Where:
- λ is the wavelength of light
- d is the separation between the slits
- L is the distance between the screen and the slits
- w is the width of the bright fringe

We are given the distance between the screen and the slits (L = 1.17 m) and the separation between the third dark fringes on either side (26.4 cm, which can be converted to meters as 0.264 m). We can assume that the distance between successive dark fringes is equal to the distance between successive bright fringes.

Using this information and rearranging the formula, we can solve for w:

w = (d * L) / λ

Since w is the width of the central bright fringe, we can assume it is the same as the separation between the dark fringes on either side. Thus, we can substitute w with 0.264 m in the above equation.

0.264 m = (d * 1.17 m) / λ

To find the value of λ, we need to know which wavelength of light is being used. Let's assume we are using visible light with a wavelength of 500 nm (500 * 10^-9 m).

0.264 m = (d * 1.17 m) / (500 * 10^-9 m)

Rearranging the equation to solve for d, the separation between the slits:

d = (0.264 m * 500 * 10^-9 m) / 1.17 m

Now, we can calculate the value of d.

d = 0.113 cm

Finally, substitute the calculated value of d back into the original equation to find the width of the central bright fringe (w):

w = (0.113 cm * 1.17 m) / (500 * 10^-9 m)

After evaluating this expression, we will have the actual value for the width of the central bright fringe.