The linear magnification of an object placed on the principal axis of a convex lens of focal length 30 cm is found to be + 2. In order to obtain a magnification of -2, by how much distance should the object be moved?

The distance between the eyepiece and the objective lens in a certain compound microscope is 10.4 cm. The focal length of the objective is 0.430 cm, and that of the eyepiece is 1.40 cm. Find the overall magnification of the microscope. (The near point of the eye is 25 cm. Assume that the object is placed at the focal point of the objective lens, and one places the eyepiece at the near point of the eye.)

An object of 1 cm tall is placed  3cm in front of a converging lens of focal length of 2 cm. (a) Use ray tracing to find the image. (b) Use the lens equation to find the image distance and compare it to your ray tracing and find the percentage error.

An object is 6 cm in front of a converging lens with a focal length of 10cm. Draw a ray diagram (to scale with a ruler) to find the location of the image. Is the image upright or inverted, and Is the image real or virtual? Then I want to use the thin lens formula to find the image distance and the magnification. I got stuck in the middle of this problem and am confused. Thank you for the help!

The projection lens in a certain slide projector is a single thin lens. A slide 23.0 mm high is to be projected so that its image fills a screen 1.90 m high. The slide-to-screen distance is 3.06 m. (Enter your answers to at least one decimal place.) (a) Determine the focal length of the projection lens. mm(b) How far from the slide should the lens of the projector be placed to form the image on the screen? mm

You are tasked with sourcing a lens which will be made out of glass with refractive index 1.668, and is submersed in a liquid with refractive index 1.379. You want a focal length of 6.5 cm, and the radius of curvature of the first side of the lens is 7.4 cm. What radius of curvature is required for the second side, in cm? [Note the first/second lens surface radius is conventionally positive/negative for convex.]

An object is placed 21.2 cm in front of a diverging lens which has a focal length with a magnitude of 13.0 cm. How far in front of the lens should the object be placed in order to produce an image that is reduced by a factor of 3.15?

A system of two lenses forms an image of an arrow at x = x3 = 57.4 cm. The first lens is a diverging lens located at x = 0 and has a focal length of magnitude f₁ = 11.5 cm. The second lens is located at x = x₂ = 25.4 cm and has an unknown focal length. The tip of the object arrow is located at (x,y) = (xo, Yo) = (-36 cm, 20.6 cm). (x,y) 1) What is x₁, the x-coordinate of image of the arrow formed by the first lens? cm Submit 2) What is y₁, the y-coordinate of the image of the tip of the arrow formed by the first lens? cm Submit X₂ Real and Inverted Real and Upright Virtual and Inverted Virtual and Upright cm Submit (+) 3) What is f2, the focal length of the second lens. If the lens is a converging lens, f2 is positive. If the lens is a diverging lens, f2 is negative. cm Submit + 4) What is y3, the y-coordinate of the image of the tip of the arrow formed by the two lens system? (+ 5) The positions of the two lenses are now interchnaged (i.e., the second lens is moved to x = 0 and the…