HW-2 Reflection, Refraction in spherical surfaces
Due date: 9/15/2025 5:00 PM PDF in D2L or hardcopy in mailbox.
(1)Use point objects and ray diagram to demonstrate the image formation
in a plane mirror. Then repeat the process for the extended length
object. Use the image formation ray diagram in refraction to explain
the bending of a straight rod in air water interface. (10 point)
(2)Show that the lateral displacement s of a ray of light penetrating a
rectangular plate of thickness t is given by
𝑡 sin(𝜃1 − 𝜃2 )
𝑠=
𝑐𝑜𝑠𝜃2
where and are the angles of incidence and refraction, respectively. Find the
displacement when t = 3 cm, n = 1.50, and 𝜃1 = 50° (10 points)
(3)Use the ray tracing in (i) convex and (ii) concave lens when object is at
2f, between f and pole. Verify the ray tracing with thin lens formula
calculation (10 points)
(4)Derive the law of reflection from Fermat’s principle by minimizing the
distance of an arbitrary (hypothetical) ray from a given source point to
a given receiving point. (5 points)
(5)A glass hemisphere is silvered over its curved surface. A small air
bubble in the glass is located on the central axis through the hemisphere
5 cm from the plane surface. The radius of curvature of the spherical
surface is 7.5 cm, and the glass has an index of 1.50. Looking along the
axis into the plane surface, one sees two images of the bubble. How do
they arise (5 points) and where do they appear? (10 points)