A positive meniscus lens (see diagram to clarify the shape of the lens) is made out...

  

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A positive meniscus lens (see diagram to clarify the shape of the lens) is made out glass and is filled with water. This forms a system of two lenses, one water and one glass in contact. The lens system is surrounded on all sides by air. Calculate an expression for the new focal length of the combined system assuming the combined system still satisfies the thin lens approximation. Use the quantities fg, fw, and fe for the focal lengths of the glass meniscus lens, the water plano-convex lens, and the combined system focal length. Note we are considering the focal lengths for the glass and water lens as if they are separate and each surrounded by air. Present your answer as an expression relating 1/f to 1/f T R₂ , and ¹/fw Step-by-step suggested solution. 1. We've just learned how to treat lenses a single optic instead of treating two spherical interfaces separately. Start by considering an object at infinity in front of the positive meniscus lens. It generates an image. The image location happens to also be equal to the second focal length of the glass lens fg. Keep your algebra simple by working with fg. 2. The water has a curved interface it also has a flat surface. Treat the water as a second thin lens! The water lens has a focal length fw (without the glass lens present and the water lens in air). 3. Imagine the water lens and the glass lens are separated by a distance d. Work out an expression for the location of the final image generated by the water image of an object at infinity. Make sure to use fg for the image distance generated by the glass lens. 4. From step three, you should now have an expression for the location of the final image generated by the two lenses combined se'. This image location also defines the second focal point for the system! 5. Set the separation of the two lenses to zero. In this case se' is now also the combined focal length for the system fe 6. Write down a compact expression relating ¹/f 1/f and 1/f for this special case of d = 0. A positive meniscus lens (see diagram to clarify the shape of the lens) is made out glass and is filled with water. This forms a system of two lenses, one water and one glass in contact. The lens system is surrounded on all sides by air. Calculate an expression for the new focal length of the combined system assuming the combined system still satisfies the thin lens approximation. Use the quantities fg, fw, and fe for the focal lengths of the glass meniscus lens, the water plano-convex lens, and the combined system focal length. Note we are considering the focal lengths for the glass and water lens as if they are separate and each surrounded by air. Present your answer as an expression relating 1/f to 1/f T R₂ , and ¹/fw Step-by-step suggested solution. 1. We've just learned how to treat lenses a single optic instead of treating two spherical interfaces separately. Start by considering an object at infinity in front of the positive meniscus lens. It generates an image. The image location happens to also be equal to the second focal length of the glass lens fg. Keep your algebra simple by working with fg. 2. The water has a curved interface it also has a flat surface. Treat the water as a second thin lens! The water lens has a focal length fw (without the glass lens present and the water lens in air). 3. Imagine the water lens and the glass lens are separated by a distance d. Work out an expression for the location of the final image generated by the water image of an object at infinity. Make sure to use fg for the image distance generated by the glass lens. 4. From step three, you should now have an expression for the location of the final image generated by the two lenses combined se'. This image location also defines the second focal point for the system! 5. Set the separation of the two lenses to zero. In this case se' is now also the combined focal length for the system fe 6. Write down a compact expression relating ¹/f 1/f and 1/f for this special case of d = 0. A positive meniscus lens (see diagram to clarify the shape of the lens) is made out glass and is filled with water. This forms a system of two lenses, one water and one glass in contact. The lens system is surrounded on all sides by air. Calculate an expression for the new focal length of the combined system assuming the combined system still satisfies the thin lens approximation. Use the quantities fg, fw, and fe for the focal lengths of the glass meniscus lens, the water plano-convex lens, and the combined system focal length. Note we are considering the focal lengths for the glass and water lens as if they are separate and each surrounded by air. Present your answer as an expression relating 1/f to 1/f T R₂ , and ¹/fw Step-by-step suggested solution. 1. We've just learned how to treat lenses a single optic instead of treating two spherical interfaces separately. Start by considering an object at infinity in front of the positive meniscus lens. It generates an image. The image location happens to also be equal to the second focal length of the glass lens fg. Keep your algebra simple by working with fg. 2. The water has a curved interface it also has a flat surface. Treat the water as a second thin lens! The water lens has a focal length fw (without the glass lens present and the water lens in air). 3. Imagine the water lens and the glass lens are separated by a distance d. Work out an expression for the location of the final image generated by the water image of an object at infinity. Make sure to use fg for the image distance generated by the glass lens. 4. From step three, you should now have an expression for the location of the final image generated by the two lenses combined se'. This image location also defines the second focal point for the system! 5. Set the separation of the two lenses to zero. In this case se' is now also the combined focal length for the system fe 6. Write down a compact expression relating ¹/f 1/f and 1/f for this special case of d = 0. A positive meniscus lens (see diagram to clarify the shape of the lens) is made out glass and is filled with water. This forms a system of two lenses, one water and one glass in contact. The lens system is surrounded on all sides by air. Calculate an expression for the new focal length of the combined system assuming the combined system still satisfies the thin lens approximation. Use the quantities fg, fw, and fe for the focal lengths of the glass meniscus lens, the water plano-convex lens, and the combined system focal length. Note we are considering the focal lengths for the glass and water lens as if they are separate and each surrounded by air. Present your answer as an expression relating 1/f to 1/f T R₂ , and ¹/fw Step-by-step suggested solution. 1. We've just learned how to treat lenses a single optic instead of treating two spherical interfaces separately. Start by considering an object at infinity in front of the positive meniscus lens. It generates an image. The image location happens to also be equal to the second focal length of the glass lens fg. Keep your algebra simple by working with fg. 2. The water has a curved interface it also has a flat surface. Treat the water as a second thin lens! The water lens has a focal length fw (without the glass lens present and the water lens in air). 3. Imagine the water lens and the glass lens are separated by a distance d. Work out an expression for the location of the final image generated by the water image of an object at infinity. Make sure to use fg for the image distance generated by the glass lens. 4. From step three, you should now have an expression for the location of the final image generated by the two lenses combined se'. This image location also defines the second focal point for the system! 5. Set the separation of the two lenses to zero. In this case se' is now also the combined focal length for the system fe 6. Write down a compact expression relating ¹/f 1/f and 1/f for this special case of d = 0.