Question

A transparent glass hemisphere with radius R and mass m has an index of refraction n. In the medium outside the hemisphere, the index of refraction is equal to one. A parallel beam of monochromatic laser light is incident uniformly and normally onto the central portion of its planar surface, as shown in Figure 3. The acceleration of gravity g is vertically downwards. The radius 8 of the circular cross-section of the laser beam is much smaller than R. Both the glass hemisphere and the laser beam are axially symmetric with respect to the z-axis. The glass hemisphere does not absorb any laser light. Its surface has been coated with a thin layer of transparent material so that reflections are negligible when light enters and leaves the glass hemisphere. The optical path traversed by laser light passing through the non-reflecting surface layer is also negligible. (6) Neglecting terms of the order (8/R) or higher, find the laser power P needed to balance the weight of the glass hemisphere. (4.0 points) Hint: cose=1-6°/2 when 0 is much smaller than one. glass hemisphere 12 R laser beam Figure 3 NA

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Answer 1

m = 2 0219 u = R 20.5m h - M=0.6 seg M Uz - The celorley of smaller ball 'n migh when it reaches I mua 2 the belton is Ug = Nagh The welwily with which Man in' ball travels como v V2 me em M et m

DATE v2 z 2 X 3 I 2 X Tagh 3 Jagh Applying ameerwalion of Senesegy for the bigger ball completing the loop Mmg (DAR) [ work done 0.6gx x (2aX0.5 2 му, z s a (2gh) against the Quillional tract 2x 49 -> ch 0.6 x x 0.5 * 2 x 49 h = 10.26 m