Coherent light of frequency 6.34×1014 hz passes through two thin slits and falls on a screen 82.0 cm away. you observe that the third bright fringe occurs at ± 3.16 cm on either side of the central bright fringeat what distance from the central bright fringe will the third dark fringe occur?

 y = 3.69 10⁻² m  = 3.69 cm

Explanation:

The interference phenomenon is described by the equations.

      d sin θ  = m λ                               for constrictive interference

      d sin θ = (m + ½) λ                       for destructive interference

Where d is the distance between the slits, m is an integer representing the order of interference λ the wavelength

Let's use the relationship

      c = λ f  

      λ = c / f

      λ = 3 10⁸ / 6.34 10¹⁴

      λ = 4.732 10⁻⁷ m

Let's use trigonometry to find the breast

    tan θ  = y / x

In interference experiments the angle is very small

     tan θ  = sin θ  / cos θ  ≈ sin θ  

We replace

    d y / x = m λ

    d y / x = (m + ½)  λ  

Let's reduce the magnitude to the SI system

       x = 82.0 cm (1m / 100 cm) = 0.820 m

       y = 3.16 cm = 0.0316 cm

Let's use the first relationship to find the distance between the slits

      d = m  λ  x / y

      d = 3 4.732 10⁻⁷ 0.820 /0.0316

      d = 368.38 10⁻⁷ m

      d = 3.6838 10⁻⁵ m

Now we can use the relationship for destructive interference and clear the distance and

        d y / x = (m + ½)  λ

        y = (m + ½)  λ  x / d

       y = (3 + ½) 4,732 10⁻⁷ 0.82 / 3.68 10⁻⁵

       y = 3.69 10⁻² m

       y = 3.69 cm

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

nah.   i'm just sleepy.