A glass rod 96 cm long with an index of refraction of 1.6 has its ends ground to convex spherical surfaces of radii 8 cm and 16 cm. A point object is in air on the axis of the rod 19.1 cm from the end with the 8 cm radius.
(a) Find the image distance due to refraction at the first
surface. (Include the sign.)
___cm
(b) Find the location of the final image distance due to refraction
at both surfaces.
___cm (from the 8 cm diameter surface)
(c) Describe the final image.
real
virtual
inside the rod
outside the rod
given that
n1 = 1 , n2 = 1.6
r = 8 cm , s = 19.1 cm
the image distance due to first surface is
s' = n2*r*s/[(n2 - n1)s - n1r] = (1.6)(8)(19.1)/ [(0.6)(19.1)-8] = 70.66 cm
the object for the second surface is the image formed by the first surface,
thus, we have
n1 = 1.6 , n2 = 1
r = -16 cm , s = 32 cm
thus the image distance due to refraction at both surfaces is
s' = n2*r*s/[(n2 - n1)s - n1r] = (1)(-16)(32)/ [(-0.6)(32)-(1.6)(-16)] = -80 cm
the final image formed is virtual
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