A cylindrical glass rod ( = 1.5 ) with a radius of 1.0 cm has one end rounded into a hemispherical shape. This rod is submerged in water ( = 4/3 ). An object is positioned in the water on the axis of the rod, 8.0 cm away from the rounded edge. Determine the location of the image of the object.

Step-by-step solution

Using the formula for refraction at a single spherical surface: ₂ v - ₁ u = ₂ - ₁ R Given: Refractive index of the surrounding medium (water), ₁ = 4 3 Refractive index of the rod (glass), ₂ = 1.5 = 3 2 Object distance, u = -8.0 cm Radius of curvature, R = +1.0 cm (positive since the center of curvature lies in the direction of incident light) Substituting the values into the formula: 3/2 v - 4/3 -8.0 = 3/2 - 4/3 1.0 3 2v + 4 24 = 9/6 - 8/6 1 3 2v + 1 6 = 1 6 3 2v = 0 v = The image is formed at infinity.