Question
Download Solution PDFWhite light reflected from a soap film (Refractive Index = 1.5) has a maxima at 600 nm and a minima at 750 nm with no minimum in between. Then the thickness of the film is ______ × 10-7 m.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- Interference: A phenomenon in which two waves superpose on each other to form a resultant wave of greater, lower, or the same amplitude is called interference.
- Thin-film interference: When light waves reflecting off from the top and bottom surfaces of a thin film interfere with another
Due to interference in Thin Films, there occurs maxima and minima.
For maxima:
\(2μ t\space cos r=\frac{(2n+1)λ_1}{2}\)
for minima:
\(2μ t\space cos r={nλ_2}\)
where μ is the refractive index of thin film, t is the thickness of soap film, r is the angle of reflection, n is the nth fringe, and λ is the wavelength.
CALCULATION:
Given that
λ1 = 600nm;
λ2 = 750 nm;
μ = 1.5
For maxima
\(2μ t\space cos r=\frac{(2n+1)λ_1}{2}\)....... (i)
for minima
\(2μ t\space cos r={nλ_2}\)............(ii)
divide eq (i) and eq (ii)
\(\frac{(2n+1)\lambda_1}{2n\lambda_2} =1\)
\(\frac{(2n+1)600}{2n\times 750} =1\)
n = 2
put in eq (ii)
\(2μ t\space cos r={nλ_2}\)
\(2×1.5× t={2× 750}\)
t = 500 nm = 5 × 10-7
so the correct answer is option 3.
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