Calculating Slit Width and Angular Deflection for 630nm and 450nm Light

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The discussion focuses on calculating the slit width and angular deflection for light wavelengths of 630nm and 450nm. For the 630nm light, the angular deflection to the tenth dark band is measured at 3.6 degrees, which can be converted to radians for calculations. The relevant equations involve the relationship between the wavelength, slit width, and angular deflection. Participants are tasked with determining the slit width using the provided angular deflection and wavelength. Additionally, they are asked to calculate the angular deflection for the 450nm wavelength using similar principles.
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Light of wavelength 630nm passes through a single slit. The angular deflection to the tenth dark band on the side of the center maximum is 3.6 degrees. A) Calculate the slit width. B) Calculate the angular deflection to the tenth dark band using light of 450 nm wavelength.

relevant Equations :

delta y = L(Lamda) over d.
 
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Convert degree into radian. Then angle theta = delta y/L = Lamda/d
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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