In Figure , POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that
`lfloorROS=(1)/(2)(lfloorQOS-lfloorPOS)`

In the given figure bar(PQ) is a line. Ray bar(OR) is perpendicular to line bar(PQ) . bar(OS) is another ray lying between rays bar(OP) and bar(OR) . Prove that angleROS = (1)/(2) angleQOS − anglePOS

If p is the length of perpendicular from origin to the line whose intercepts on the axes are 'a' and 'b' then prove that (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

In the adjacent figure ray OS stands on a line PQ. Ray OR and ray OT are angle bisectors of anglePOS and angleSOQ respectively. Find angleROT .

In the figure, if trianglePOQ - triangleSOR and PQ: RS= 1:2, then OP: OS is

In the given Figure , PQ and RS are two mirrors placed parallel to each other . An incident ray AB striker the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB|| CD.

In the given figure, name (i) any six points (ii) any five line segments (iii) any four rays (iv) any four lines (v) any four collinear points

A ray of light falls on a transparent sphere sphere with centre C as shown in the figure. The ray emerges from the sphere parallel to the line AB. Find the angle of refraction at A, if refractive index of the material of the sphere is sqrt(3) .

Draw ray diagrams showing the image formation by a convex lens when an object is placed (a) between optical centre and focus of the lens (b) between focus and twice the focal length of the lens OR Draw the ray diagram when the object is kept between F_(1) and 2F_(1) of the convex lens. With the help of the diagram mention the position and nature of the image formed. [ F_(1) : Principal focus of the lens] (c ) at twice the focal length of the lens (d) at infinity (e ) at the focus of the lens