Question

Light travels from one medium at an angle of incidence 45 degrees to another medium making an angle of reflection 30 degrees the ratio of refractive index is half to media it​

Answer 1

Given :

Angle of incidence = 45°

Angle of refraction = 30°

To Find :

The ratio of refractive index of two media.

Concept :

★ Law of Refraction :

• The incident ray, the normal to any refracting surface at the point of incidence and the refracted ray all lie in the same plane of incidence or plane of refraction.
• sini/sinr = constant for any pair of media and for light of a given wavelength. This is known as snell's law.

Formula : $\underline{\boxed{\bf{\orange{n_1sin(i)=n_2\sin(r)}}}}$

Calculation :

$:\implies\tt\:n_1sin(i)=n_2sin(r)$

$:\implies\tt\:n_1sin45^{\circ}=n_2sin30^{\circ}$

$:\implies\tt\:n_1\times\dfrac{1}{\sqrt2}=n_2\times\dfrac{1}{2}$

$:\implies\tt\:\dfrac{n_1}{n_2}=\dfrac{\sqrt2}{2}$

$:\implies\bf\:n_1:n_2=1:\sqrt2$

Answer 2

Answer:

♠️ QuEsTiOn ♠️

Light travels from one medium at an angle of incidence 45 degrees to another medium making an angle of reflection 30 degrees the ratio of refractive index is half to media it

♠️ To find ♠️

the ratio of refractive index is half to media it

♠️ FormUla♠️

$n1 \sin(i)</strong><strong> </strong><strong>=</strong><strong> </strong><strong>N2</strong><strong> </strong><strong>\</strong><strong>s</strong><strong>i</strong><strong>n</strong><strong>(</strong><strong>r</strong><strong>)</strong><strong> </strong><strong>$

♠️ Solution ♠️

$n1 \sin(45) = n1 \sin(30)$

$n1 \times \frac{1}{ \sqrt{2} } </strong><strong>=</strong><strong> </strong><strong>n2</strong><strong> </strong><strong>\</strong><strong>t</strong><strong>i</strong><strong>m</strong><strong>e</strong><strong>s</strong><strong> </strong><strong>\</strong><strong>f</strong><strong>r</strong><strong>a</strong><strong>c</strong><strong> </strong><strong>{</strong><strong>1</strong><strong>}</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong> </strong><strong>$

$\frac{n1}{n2 =}$ $\frac{ \sqrt{2} }{2}$

Ratio 1: √2