Exams › JEE Advanced › Physics

A coin rests at the bottom of an empty hemispherical bowl of radius R. An observer looking over the rim of the bowl can just barely not see the coin. When the bowl is completely filled with water (refractive index mu), the entire coin becomes just visible to the same observer in the same position. Find the diameter of the coin.

1. 2R*(mu² - 1) / (mu² + 1)
2. 2R*(mu - 1) / (mu + 1)
3. R*(mu² - 1) / (mu² + 1)
4. R*(mu - 1) / (mu + 1)

Correct answer: 2R*(mu² - 1) / (mu² + 1)

Solution

With an empty bowl, the line of sight from the rim just grazes the far edge of the coin. When water is added, refraction at the surface bends the ray so the coin's near edge also becomes visible. Applying Snell's law at the point where the ray exits the water surface at the rim, and using the hemispherical geometry (depth = R, radius = R), yields D = 2R*(mu²-1)/(mu²+1).

Related JEE Advanced Physics questions

• The image of an object, formed by a plano-convex lens at a distance of 8m behind the lens, is real and is one third the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free space. The radius of the curved surface of the lens is -
• When two waveguides with identical cross-sectional areas but differing numerical apertures, NA₁ and NA₂ (where NA₂ is smaller than NA₁), are connected end-to-end, the resulting numerical aperture of the system is:
• A point light source is submerged inside water (refractive index n = 4/3). When the source is at depth H below the surface, the fraction of total light energy that escapes out of the water is 'a'. When the same source is placed at depth 2H, the fraction that escapes is 'b'. Which of the following correctly relates a and b?
• A cylindrical bucket of depth 60 cm is partly filled: the bottom third (20 cm) contains a liquid of refractive index 1.5 and the middle third (20 cm) contains oil of refractive index 2. The top third (20 cm) is air. To an observer looking vertically downward from the top, the volumes of air, liquid and oil appear equal. The apparent depth of the bucket as seen by the observer is alpha cm. Find alpha/5.
• A point light source S sits at the bottom of a stack of plane-parallel layers. The bottommost layer has refractive index mu0. The n-th layer above the bottom has refractive index mu(n) = mu0 + mu0/(4n - 18). A ray leaves S at an angle of incidence i = 30° measured from the vertical. At the upper surface of which layer does total internal reflection (TIR) first occur?
• A converging lens forms a real image of an object on a fixed screen. The lens is then moved at constant speed v0 along its principal axis away from the screen while the object is simultaneously moved to keep the image on the screen at all times. If the image size is twice the object size at some instant, what is the required speed of the object at that instant?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →