A transparent hemisphere of refractive index 1.5 and radius of curvature 20 cm is placed flat side down on a piece of paper with a 4.0 mm tall letter G written on it such that G is in the center.What is the size of G when viewed directly from above

A negatively charged ion is travelling eastward with a velocity of 7000 m.s−1 when it passes through a region of magnetic field of strength 0.04 T which is directed vertically upwards. The direction of the force on the negative ion is:

I am not sure northward or vertically upward if someone can explain

Your answer quite unrelated

To find the size of the letter G when viewed directly from above, we need to consider the refraction of light at the interface between the air and the transparent hemisphere.

Here are the steps to find the size of the letter G:

1. Begin by drawing a diagram. Draw the hemisphere and place the letter G on the paper beneath it. Label the relevant dimensions: the radius of curvature of the hemisphere (r = 20 cm) and the height of the letter G (h = 4.0 mm).

2. Determine the angle of refraction. The angle of incidence, i, is the angle between the incident ray and the normal to the interface (which is a horizontal line in this case). Since the hemisphere is flat side down, the normal is vertical. So the angle of incidence, i, is 90 degrees. The refractive index, n, is given as 1.5. The angle of refraction, r, can be found using Snell's law:

n₁ * sin(i) = n₂ * sin(r)

Here, n₁ = 1 (the refractive index of air, which can be approximated as 1) and n₂ = 1.5 (the refractive index of the hemisphere). Therefore, the equation becomes:

1 * sin(90°) = 1.5 * sin(r)

sin(r) = (1 * sin(90°)) / 1.5
sin(r) = 1 / 1.5

Taking the arcsin of both sides to find r:

r = arcsin(1 / 1.5)
r ≈ 41.81°

3. Calculate the bending angle, b. The bending angle is the angle of incidence minus the angle of refraction:

b = i - r
b = 90° - 41.81°
b ≈ 48.19°

4. Find the actual height of the letter G, h'. The actual height is the height of the letter G, h, divided by the magnification, M:

M = 1 / sin(b)
h' = h / M
h' = h / (1 / sin(b))
h' = h * sin(b)
h' ≈ 4.0 mm * sin(48.19°)

Using a calculator or trigonometric table, calculate h' to find the size of the letter G when viewed directly from above.

Note: Make sure to convert the units to be consistent throughout the calculation (e.g., cm or mm).