Understanding double slit experiment; formula relationship

[dahmsom]

Lets say if a double slit were to be put into water.
I understand that water has a bigger index of refraction than air so thus if you put a double slit into water you will get a smaller wavelength; because as the index of refraction increases wavelength decrease.

Using the double slit formula; m (wavelength)= d sin Theta. You see that wavelength gets smaller the angle gets smaller making the the bright fringe closer together. Im not understand where in the formula shows bright fringe getting closer, cause i thought the D represents the length of the slit. And if thetha gets smaller does the "D" get bigger? how do i know that the bright fringe is getting closer together based on the formula?

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[ElectricNoogie]

Hello @dahmsom !

If you take Young's Experiment and take it underwater, it is still light we are observing. What happens to the wavelength of light as it enters water? The wavelength should decrease (this can be explained as the speed of light is decreasing, but the frequency cannot change, so it must be a change in wavelength).

As for your D values, using the setup below, we can see that the fringes not only demonstrate the wave nature of light, they also allow the wavelength to be measured.

Wavelength is lambda .
Distance between the two slits s1 and s2 is d.
Distance between the source screen and the observation screen is D.
Extra distance that the light passing through s1 travels is d sinθ.

Placing the apparatus in water should not affect d nor D. Regarding the space between fringes, we can say that for two neighboring bright lines, the angles differ by:

Δθ=lambda/d.

The spacing between the fringes is: ΔθD =lambda(D/d) where D/d is known as the amplification number.

Thus, as d increases the spacing between the fringes gets smaller so to see large fringes, we need a small d. For larger wavelengths we need a large path difference to have a change of phase so the distance between fringes is larger. The opposite is true for smaller wavelengths. Finally D, if the screen is further, for a fixed angle, the spacing between the fringes gets larger.

Hope this helps, good luck!