Diameter of [tex]25^{th}[/tex] Newton Ring = 0.97 cm
Newton Rings is an experiment based on principle of thin film interference
In Newton Rings Experiment the Diameter of [tex]n^{th}[/tex] dark ring is given by equation (1)
[tex]\rm D_n= 2\sqrt{n\lambda R} ......(1)\\where \; \\D_n = Diameter\; of \; n^{th} \; dark \; ring }\\n = Number \; of \; Ring\\\lambda = Wavelength \\R = Radius \; of \; Curvature \; of\; the \; lens[/tex]
From the condition given
[tex]\rm D_5 = 0.3 \; cm \\D_{15} = 0.62 \; cm\\\\D_{25} = To \; be \; determined \\[/tex]
Putting the values in equation (1) for fifth diameter we get
[tex]\rm D_5 = 0.3=2\sqrt{5\lambda R}.......(2) \\D_{15} = 0.62 = 2\sqrt{15\lambda R}.......(3) \\\\Equation \; (3) - Equation (2) \\\\0.32 = 2\sqrt{\lambda R} ( \sqrt{15} -\sqrt{5})\\\\2\sqrt{\lambda R } = 0.1954....(4)\\[/tex]
So From equation (1) and (4)
[tex]\rm Diameter \; of \; 25^{th} Ring =D_{25} = 2\sqrt{\lambda R } \times \sqrt{25} \\\\D_{25} = 0.1954\times 5 \\\\D_{25} = 0.97 \; cm[/tex]
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