In Young's double slit experiment, the brightness of the bright fringes does not change if the wavelength is increased. The intensity or brightness of the fringes depends on the square of the amplitude of the resulting interference pattern.
The interference pattern in the double slit experiment is formed due to the constructive and destructive interference of waves from the two slits. The bright fringes occur where the waves from the two slits constructively interfere, resulting in a maximum intensity of light. The dark fringes, on the other hand, occur where the waves destructively interfere, resulting in minimum or zero intensity.
The position of the fringes is determined by the wavelength of the light used in the experiment, according to the equation for constructive interference:
d * sin(theta) = m * lambda,
where d is the slit separation, theta is the angle of the fringe, m is an integer representing the order of the fringe, and lambda is the wavelength of light.
If the wavelength is increased, the angle theta corresponding to each fringe will increase as well. However, the distance between adjacent fringes (the fringe separation) remains the same, as it is determined by the slit separation and does not depend on the wavelength.
Therefore, increasing the wavelength does not affect the brightness or intensity of the bright fringes. The brightness remains the same, but the positions of the fringes will be shifted to larger angles.