An equiconvex lens having spherical surfaces of radius 10 cm, a central thickness of 2 cm, and a refractive index of 1.61 is situated between air and water (n = 1.33). An object 5 cm high is placed 60 cm in front of the lens surface. Find the cardinal points for the lens and the position and size of the image formed.
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- A lens system consists of a +4D lens and a +3D lens separated by 10 cm. Find the equivalent focal power and the positions of the principal points. An object 3 cm long is situated 50 cm in front of the first lens. What will be the position and size of the image produced by the combination?Figure shows a simple version of a zoom lens. The converging lens has focal length f1 and the diverging lens has focal length f2 = -Ι f2Ι. The two lenses are separated by a variable distance d that is always less than f1. Also, the magnitude of the focal length of the diverging lens satisfies the inequalityΙ f2Ι7( f1 - d). To determine the effective focal length of the combination lens, consider a bundle of parallel rays of radius r0 entering the converging lens. (a) Show that the radius of the ray bundle decreases to r′ 0 = r0( f1 - d)/f1 at the point that it enters the diverging lens. (b) Show that the final image I′ is formed a distance s′ 2 =If2I( f1 - d)/(I f2I- f1 + d) to the right of the diverging lens. (c) If the rays that emerge from the diverging lens and reach the final image point are extended backward to the left of the diverging lens, they will eventually expand to the original radius r0 at some point Q. The distance from the final image I′ to the point Q is the…A lens of focal length +24.0 cm is at x 0, and a second lens of focal length -24.0 cm is located at x = 16.0 cm. Let the positive x-direction be to the right. At what position x is the final image of an object that is 48.0 cm to the left of the positive lens? cm X = What is the magnification m of the image?.(Remember that magnification can be positive or negative.) m = The image is and virtual real Where should your eye be located and directed to see the image? O looking left from the right of both lenses looking left from between the lenses looking right from between the lenses O looking right from the left of both lenses Question Source: Freedman College Physic
- A thick-walled wine goblet can be considered to be a hollow glass sphere with an outer radius of 4.10 cmcm and an inner radius of 3.60 cmcm. The index of refraction of the goblet glass is 1.50. (a) A beam of parallel light rays enters the side of the empty goblet along a horizontal radius. Where, if anywhere, will an image be formed? (b) The goblet is filled with white wine (nn = 1.37). Where is the image formed? Use the image from the previous part as the object for the second surface (the inner wall of the same side of the goblet) and find the position of the second image. Express your answer with the appropriate units.A little fish of 1 cm of height is at the center of a spheric fishbowl with diameter of 20 cm filled with water (n=1.33). The material of the sphere is so thin that its effects of refraction can be neglected. A thick equiconvex lens with thickness 2 cm and radii of curvature of 15cm and refraction index of 1.5 is located with its first vertex at a distance of 50cm of the center of the bowl. What is the position on the optic axis of the image of the fish? What is the size of the imageTwo lenses are placed along an optical rail. One is a converging lens, with a focal length of f1 = 30.3 cm. The second lens, a diverging lens with a focal length of f2 = −20.0 cm, is placed d = 110 cm to the right of the converging lens. An object ho = 2.02 cm high is placed p1 = 40.5 cm to the left of the converging lens. (a) Determine the position of the final image. (Enter the position in cm relative to the diverging lens.) magnitude ? cm direction right or left? of the diverging lens (b) Determine the magnification of the final image. (Indicate the orientation with the sign of your answer.) Hint* The total magnification is the product of each individual magnification. (c) Is the image upright or inverted? (d) Repeat parts (a) through (c) for the case in which the second lens is a converging lens having a focal length of 20.0 cm. (Enter the position in cm relative to the second lens. Indicate the orientation of the magnification with the sign of your…
- Compute the focal length of a diverging thin lens made of flint glass, whose refractive index is 1.66 and is immersed in air having refractive index 1. The radii of the spherical surfaces of the lens are 10 cm and 20 cm. Select one: O -30 cm O O -10 cm 30 cm 10 cmA 1 [cm] tall object is 50 [cm] away from a converging lens of focal length f = 30 [cm]. A second converging lens of focal length f = 80 [cm] is placed 2 [m] behind the first lens. a) Where is the image formed by the first lens (ignoring the second lens)? How big is it? b) Now, this image is the object for the second lens. Where is the second (final) image formed by the second lens? How big is it?An object is placed 25 cm in front of a converging lens of focal length 20 cm. 30 cm past the first lens is a second diverging lens of magnitude focal length 25 cm. What are the resulting image position relative to second lens and total magnification of the object in this setup?
- A 1.00-cm-high object is placed 3.95 cm to the left of a converging lens of focal length 7.80 cm. A diverging lens of focal length –16.00 cm is 6.00 cm to the right of the converging lens. Find the position and height of the final image. position 7.5 cm in front of the second lens v 0.5466 height Calculate the magnification produced by each lens. Then consider how the magnification relates image size and object size for each lens to find the height of the final image. cm Is the image inverted or upright? upright O inverted Is the image real or virtual? real virtualAn 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.A laser beam of diameter d₁-1.1 mm is directed along the optical axis of a thin lens of focal length +4.7 cm (see figure below). (a) How far from the lens will the beam be focused? (b) A second positive lens is placed to the right of the first. Light emerges from the second lens in a parallel beam of diameter dy 3.6 mm. Thus the combination of lenses acts as a beam expander. Find the focal length of the second lens. Find the distance between the lenses.