a)
As per the given question,
wavelength of the yellow light "(\\lambda)=589.3nm= 589.3\\times 10^{-9}m"
"\\lambda_1=435nm"
Angle"=105.4^\\circ"
"d\\sin\\theta = n\\lambda"
"\\Rightarrow d=\\dfrac{n\\lambda}{\\sin\\theta}=\\dfrac{7\\times 589.3\\times 10^{-9}}{\\sin{105.4^\\circ}}" m
"m=\\dfrac{d\\sin\\theta}{\\lambda_1}=\\dfrac{7\\times 589.3\\times 10^{-9}\\sin{105.4^\\circ}}{\\sin{105.4^\\circ}\\times435\\times 10^{-9}}"
"=\\dfrac{7\\times 589.3}{435}=9"
b) n=5
angle "(\\theta)=94.1^\\circ"
"d=1.67 microns=1.67\\times 10^{-6}m"
"d\\sin\\theta= n\\lambda"
"\\lambda = \\dfrac{d\\sin \\theta}{n}=\\dfrac{1.67\\times 10^{-6}\\sin(94.1)}{5}"
"\\lambda = 0.33\\times 10^{-6}m"
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