Three transparent media having refractive indices ₁ , ₂ , and ₃ are shown in the figure. A point object O is located in the medium ₂ . When the entire medium to the right of the spherical surface has a refractive index ₁ , the image is formed at O' . When this entire medium has a refractive index ₃ , the image is formed at O'' . Under the conditions depicted,

Step-by-step solution

When light rays from the object O fall on the spherical surface, they are refracted by two different media on the right side. For the upper half of the spherical surface, the light travels from the medium of refractive index ₂ to the medium of refractive index ₃ . The refraction formula is given by: ₃ v_ upper - ₂ u = ₃ - ₂ R This is identical to the case where the entire right medium has a refractive index ₃ . Thus, the rays passing through the upper half will form an image at O'' . For the lower half of the spher