A point-like light-source is placed (in air) to the symmetry axis of a hemisphere shaped piece of glass of radius 20 cm, 10 cm away from the plane surface. The refractive index of glass is 1.5. If a r

Question

A point-like light-source is placed (in air) to the symmetry axis of a hemisphere shaped piece of glass of radius 20 cm, 10 cm away from the plane surface. The refractive index of glass is 1.5. If a ray travels a distance x (in cm) through the glass till it reaches the curved surface as shown in figure then find the value of $\frac{2 + 1}{5} x$ .

TestHub · Accepted Answer

From the geometry in the figure: cos ( 9 0 ∘ + θ ) = 2 x ( 10 3 ​ ) x 2 + ( 10 3 ​ ) 2 − R 2 ​ = − 3 ​ 1 ​ With R = 20 cm: x 2 + 20 x − 100 = 0 ⇒ x = 10 ( 2 ​ − 1 ) c m 5 2 ​ + 1 ​ x = 5 ( 2 ​ + 1 ) × 10 ( 2 ​ − 1 ) ​ = 2

Physics - Geometrical Optics Question with Solution | TestHub

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