Calculate the angle of the total internal reflection theta_c (critical angle) in

Question

Calculate the angle of the total internal reflection theta_c (critical angle) inside the Crown glass (n_g = 1.52) at the boundary with water (use n_w = 1.33 for the refractive index of the water). A positive (convex) lens has focal length f = 150 mm. A small object of size y_0 = 1 cm is placed at the distance d_0 = 250 mm away from the lens. Calculate the size of the image y_i, and the distance of the image from the lens d_i. Is this image real or virtual? Is this image inverted? A negative (concave) lens has focal length f = -100 mm. A small object of size y_0 = 1 cm is placed at the distance d_0 = 300 mm away from the lens. Calculate the size of the image y_i, and the distance of the image from the lens d_i. Is this image real or virtual? Is this image inverted?

Explanation / Answer

2. given refractive index of crown glass, ng = 1.52
refractive index of water, nw = 1.33
now for critical angle
sin(ic)/sin(90) = 1.33/1.52
ic = 61.044 deg

3. given, for convex lens
f = 150 mm
yo = 1 cm
object distance, do = -250 mm
let image distance be yi and image hieght be yi
then from lens formula
1/v + 1/u = 1/f
1/di - 1/250 = 1/150
di = 93.75 mm
now, di/do = yi/yo
yi = 0.375 cm
4. f = -100 mm
yo = 1cm
do = -300 mm
1/di + 1/do = 1/f
1/di = -1/100 + 1/300
di = -150 mm
and yi = 0.5 cm

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