Distance possible between a real object and its real image

Question

•  1.  Demonstrate that the minimum distance possible between a real object and its real image through a thin convex lens is 4f, where f is the focal length of the lens.

 

• 2.An air-filled cavity bound by two spherical surfaces is created inside a glass block. The two spherical surfaces have radii R₁ = 34.4 cm and R₂ = 21.0 cm, respectively, and the thickness of the cavity is d = 41.2 cm (see diagram below). A light-emitting diode (LED) is embedded inside the block a distance of 60.0 cm in front of the cavity. Given n_glass = 1.50 and n_air = 1.00, and using only paraxial light rays (i.e., in the paraxial approximation) do the following. (The paraxial approximation is a small angle approximation so sin(θ) ≈ θ. This applies to both the incident angles and refracted angles.) (a) Calculate the final position of the image of the LED through the air-filled cavity. (b) Draw a ray diagram showing how the image is formed. Ans:- 48.2 cm, to the left of the second surface.

 

•   3. Two lenses are used to create an image for a source 10.0 cm tall that is located at d_o = 31.0 cm to the left of the first lens, as shown in the figure below. Lens L₁ is a biconcave lens made of crown glass (index of refraction n = 1.55) and has a radius of curvature of 20.0 cm for both surface 1 and 2. Lens L₂ is d = 39.0 cm to the right of the first lens L₁. Lens L₂ is a converging lens with a focal length f = 30.5 cm. At what distance relative to the object does the image get formed? Determine this position by sketching rays and calculating algebraically. Ans:- 77.1 cm, to the right of lens L₂

 

• 4.  Some reflecting telescope mirrors utilize a rotating tub of mercury to produce a large parabolic surface. If the tub is rotating on its axis with an angular frequency ω, show that the focal length of the resulting mirror is: f = g/2ω².

5.    Jack has a near point of 30.2 cm and uses a magnifier of 27.0 diopter. (a) What is the magnification if the final image is at infinity? (b) What is the magnification if the final image is at the near point? Ans:- 8.15, 9.15.

•         A diverging lens with f = −28.0 cm is placed 16.1 cm behind a converging lens with f = 21.6 cm. Where will an object at infinity in front of the converging lens be focused? Ans:- 6.84 cm