Final answer:
The separation between the first order bright fringes produced by violet and red light, passed through a diffraction grating and onto a screen 3.04 meters away, can be calculated using the diffraction grating formula relating grating spacing, wavelength, and diffraction angle.
Step-by-step explanation:
The student is asking to determine the separation on the screen between the first order bright fringe produced by the violet light and that produced by the red light after passing white light through a diffraction grating with 105 lines/cm, with the screen being 3.04 m away.
To calculate the separation, we use the formula for diffraction grating: d sin(\(\theta\)) = m\(\lambda\), where d is the distance between adjacent slits (grating spacing), \(\theta\) is the diffraction angle, m is the order of the bright fringe (which is 1 in this case), and \(\lambda\) is the wavelength of the light.
First, we calculate the grating spacing (d) from the given line density: d = 1 cm / 105 lines = 10-5 cm = 10-7 m. Next, we can find the angles for violet (\(\lambda=385 nm\)) and red (\(\lambda=654 nm\)) light using the equation above, then use the trigonometric relationship L = \(\theta\) * distance to the screen to find the position of each bright fringe on the screen. The separation is the difference between these positions.