An observer looks at a distant tree of height $$10$$ $$m$$ with a telescope of magnifying power of $$20.$$ To the observer the tree appears:

Monochromatic light is incident on a glass prism of angle $$A$$. If the refractive index of the material of the prism is $$\mu $$, a ray, incident at an angle $$\theta $$. on the face $$AB$$ would get transmitted through the face $$AC$$ of the prism provided :

A green light is incident from the water to the air - water interface at the critical angle $$\left( \theta \right)$$. Select the correct statement.

A thin convex lens made from crown glass $$\left( {\mu = {3 \over 2}} \right)$$ has focal length $$f$$. When it is measured in two different liquids having refractive indices $${4 \over 3}$$ and $${5 \over 3},$$ it has the focal lengths $${f_1}$$ and $${f_2}$$ respectively. The correct relation between the focal lengths is :