Two identical converging lenses 1 and 2, each having a focal length F, are arranged as shown in figures. The principal axes of both are parallel and separated by h. Find the distance between source S and final image. The distance between source and its final image after emerging out of both lens is $\frac{1}{2}\sqrt{X{F}^2+h^2}.$ Fill in the value of $\sqrt{X}$ 
 

Consider two rays coming from a light source. Let the first ray travel, coinciding with the optical axis of the first lens. It will pass through this lens without refraction. The second lens will refract the beam so that it intersects its optical axis at its same focus. Let the second ray go to the point of intersection of the plane of the first lens with the optical axis of the second lens. Since the source is located at double the focal length from the lens, after refraction this ray will go symmetrically to the incident one, and after the second refraction it will go parallel to the optical axis of the second lens (since it leaves its focus). 
$S{S}^{\text{'}}=(1/2)\sqrt{49F^2+h^2}$