Radii of Bright Fringes in Reflected Light for Plano-Convex Lens

[snoweangel27]

Homework Statement

A plano-convex glass lens of radius of curvature 2.6 m rests on an optically flat glass plate. The arrangement is illuminated from above with monochromatic light of 565-nm wavelength. The indexes of refraction of the lens and plate are 1.6. Determine the radii of the first and second bright fringes in the reflected light.

Homework Equations

t=1/4 lamda
x = \sqrt{2tR}

The Attempt at a Solution

I calculated the first fringe to be 8.5703e-4m. I thought that I would be able to calculate the first dark spot using t= 1/2 lamda and subtract the two to obtain the difference. However, I am not getting the right answer. Does anyone know if this is the correct method and equation?

 

[alphysicist]

Hi snoweangel27,

The formula you have (t=(1/4) lambda) arises from finding the minimum thickness giving constructive interference, and it looks like you correctly found the radius corresponding to this first bright fringe.

There's no need to find the first dark fringe (although your equation t= 1/2 lambda is correct for that). Instead, find the thickness expression for the second bright fringe, and then find its radius the same way you did for the first bright fringe.