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A transpar ent rod 40 cm long is cut flat at one end and rounded to a hemispherical surface 12 cm radius at the other end. A small object is embedded within the rod along its axis and half way between its ends. When viewed from the flat end of the rod, the object appears 10 cm deep. What is its apparent depth when viewed from the curved end? |
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Answer» Solution :Case I: When the object is viewed from the flat surface:Real depth of the object = 20 cm Apparent depth = 10 cm Using, `mu=("Real Depth")/("Apparent Depth")` We have`mu=20/10=2` Case II: When the object is viewed through the CURVED surface: Here therefraction is TAKING PLACE at the single curved surface.So we will use `mu_(2)/v -mu_(1)/u=(mu_(2)-mu_(1))/R` Here, `mu_(1)=2, mu_(2)=1,u=-20cm,v=?,R=-12cm` `1/v-2/((-20))=(1-2)/(-12)` `1/v=1/12 - 1/10` `1/v=(10-12)/120 = (-2)/120` `impliesv=60cm` Hence the object appears 60 cm deep from the curve surface.  
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