Question

A researcher measures the thickness of a layer of benzene (nn = 1.50) floating on water by shining monochromatic light onto the film and varying the wavelength of the light. She finds that light of wavelength 525 nmnm is reflected most strongly from the film. What does she calculate for the minimum thickness of the film?

Answer 1

Answer:

The minimum thickness is $t= 8.75*10^{-8} m$

Explanation:

generally the equation for thin film interference is mathematically represented as

            $2nt = (m + \frac{1}{2} ) \lambda$

Where t the  thickness  

           m is any  integer

            n is the refractive index of the film

            $\lambda$ is the wavelength of light

Since we are looking for the thickness we make t the subject of the  formula

          $t = \frac{(m+ \frac{1}{2} ) \lambda}{2n}$

m= 0 cause the thickness is minimum at m=0

   Substituting values

                    $t = \frac{(0 +\frac{1}{2}) 8525*10^{-9} }{2 *1.5}$

                       $t= 8.75*10^{-8} m$

Answer 2

Answer:

8.75e-8m

Explanation:

The thickness of the film for the constrctive interference is represented as : 2t = ( m + 0.5 ) λ*

Where λ* is the new wavelength and it is represented as

λ* = λ÷μ

The minimum thickness of the film is represented as t*. At m = 0

2tmin = ( 0 + 0.5 ) × ( 525e-9 )/1.50

2tmin = 0 + 262.5e-9/1.50

2tmin × 1.50 = 2.625e-7

3tmin = 2.625e-7

tmin = ( 2.625e-7 ) ÷ 3

tmin = 0.875e-7

tmin = 8.75e-8m