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A concave mirror of radius 40cm lies on a horizontal table and water is filled in it up to a height of 5.00 cm. A smalll dust particles floats on the water surface at a point P vertically above the point of contact of the mirror with the table. Locate the image of the dust partical as seen from a point directly above it . The refractive index of water 1.33. |
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Answer» Solution :The ray diagram is shown in the following FIGURE. Let us first locate the mage FORMED by the concave mirror. Let us take vertically upward as the negative axis. Then, `R=-40cm.` The OBJECT distance is `u=-5cm. ` Using the mirror equation: `(1)/(u)+(1)/(v)=(2)/(R)` `(1)/(v)=(2)/(R)-(1)/(u)=(2)/(-40cm) -(1)/(-5cm)=(6)/(40)cm` or `v=6.67cm` The positivesign shows that the image `P_(1)` is formed below the mirror and hence, it is virtual. These reflected rays are REFRACTED at the water SURFACE and go to the observer. The depth of the point `P_(1)` from the surface is `6.67 cm +5.00cm=11.67cm.` Due to refraction at the water surface, the image `P_(1)` will be shifted above by a distance (`11.67` cm) `(1-(1)/(1.33))=2.92cm` Thus, the final image is formed at a point`(11.67-2.92)cm =8.75cm` below the water surface. 
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