A concave mirror of radius 40 cm lies on the horizontal table and water is filled in it joto height of 5 cm a small dust particle floats on water surface vertically above the point of contact of the mirror with the table location of the image of the dust as seen from a point directly above it
Answers
Answer:
Explanation:
=> For the image formed by concave mirror:
object distance, u = -5 cm.
radius, R = -40 (suppose the image formed by concave mirror is vertically upward)
=> By using mirror equation,
1/u + 1/v = 2/R
1/v = 2/R - 1/u
1/v = 2/-40 - 1/-5
1/v = 6/40 cm
∴ v = 6.67 cm
=> This image I1 is formed at 6.67 cm behind the mirror. It is virtual image.
=> here, the reflected rays are reflected by the water surface and reach the viewer.
the deepness of the point I1 from the surface is,
6.67 cm + 5 cm = 11.67 cm
=> the image I1 will be shifted above due to the refraction at water surface,
distance of image formed due to refraction: 11.67 * 1-1/1.33 = 2.92 cm.
=> therefore, the final image is formed at 11.67 cm - 2.92cm = 8.75 cm beneath the water surface.
here, 8 + a/4 = 8.75
a/4 = 8.75 - 8
a/4 = 0.75
a = 0.75 * 4
∴ a = 3