Light from a point source in air falls on a convex curved surface of radius $20 \,cm$ and refractive index $1.5$. If the source is located at $100 \,cm$ from the convex surface,the image will be formed at what distance from the object?

The figure shows a transparent sphere of radius $R$ and refractive index $\mu$. An object $O$ is placed at a distance $x$ from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface. If $x = 2R$,then the value of $\mu$ is

The given figure shows a ray of light passing through two media having refractive indices $4/3$ and $3/2$ respectively. The ratio of times taken by the ray in traversing the distances $AB$ and $BC$ is

Consider a point object $O$ situated at a distance of $30 \ cm$ from the centre of a sphere of radius $2 \ cm$ and refractive index $\mu_2 = 1.5$ as shown in the figure. If the refractive index of the region surrounding this sphere is $\mu_1 = 1.4$,then the position of the image due to refraction by the sphere with respect to the centre is:

An air bubble in a glass sphere $(\mu=1.5)$ is situated at a distance $3\; cm$ from a convex surface of diameter $10\; cm$. At what distance from the surface will the bubble appear (in $; cm$)?

The figure shows a transparent sphere of radius $R$ and refractive index $\mu$. An object $O$ is placed at a distance $x$ from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface. If an object is placed at a distance $R$ from the pole of the first surface,then the real image is formed at a distance $R$ from the pole of the second surface. The refractive index $\mu$ of the sphere is given by