Optics IIT JEE
A tarantula of height h sits cautiously before a spherical mirror whose focal length has absolute value 40 cm. The image of the tarantula produced by the mirror has the same orientation as the tarantula and has height 0.20 times of h. (a) Is the image real or virtual, and is it on the same side of the mirror as the tarantula or the opposite side? (b) Is the mirror concave or convex, and what is its focal length with sign?
a) Since the image is erect(same orientation) so it is a virtual image. It is formed on the opposite side of the mirror since it is virtual and erect and smaller than the tarantula. b)The mirror is convex because the image is virtual and erect which is always formed by the convex mirror and the virtual image formed by a concave mirror is larger than the object but here it is smaller so it is convex. The focal length is +40cm.
A Jurassic mosquito is discovered embedded in a chunk of amber, which was index of refraction 1.6. One surface of the amber is spherically convex with radius of curvature 3.0 mm. The mosquito head happens to be on the central axis of that surface and, when viewed along the axis, appears to be buried 5.0 mm into the amber. How deep is it really?
n2/v-n1/u=n2-n1/R => 1.6/5-1/u=1.6-1/3=> u=8.33mm