Consider a convex lens having a thickness d whose sides have radii of curvature R1 and R2. a. Find the 2x2 matrix describing this lens b. What is the change in focal length for the case where the two radii equal R and d =0.1R, compared to the case where the lens thickness is neglected?
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Consider a convex lens having a thickness d whose sides have radii of curvature R1 and
R2.
a. Find the 2x2 matrix describing this lens
b. What is the change in focal length for the case where the two radii equal R and
d =0.1R, compared to the case where the lens thickness is neglected?
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- Some telephoto cameras use a mirror rather than a lens to magnify distant objects. What radius of curvature R, in meters, does the mirror need to have to replace a 550 mm focal length telephoto lens?An optician is designing a contact lens. The material has is an index of refraction of 1.45. In order to yield the prescribed focal length, the optician specifies the following dimensions: inner radius of curvature = +2.60 cm outer radius of curvature = +1.98 cm where the inner radius of curvature describes the surface that touches the eye, and the outer radius of curvature describes the surface that first interacts with incoming light. What is the focal length of this contact lens (in cm)?b,c,d
- Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is p5 = +24 centimeters, the type of mirror is convex, and then the distance between the focal point and the mirror is 44 cm (without proper sign). Find (a) the radius of curvaturer (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side. (a) Number i (b) Number i (c) Number (d) (e) (f) MI Units Units UnitsThe lens in the figure below is made of glass of index 1.50 and have surfaces with radii of curvature of magnitude either 9.40 cm or 21.3 cm. Find the radii of curvature and the focal length of the lens.Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +20 cm, the type of mirror is concave, and then the distance between the focal point and the mirror is 13 cm (without proper sign). Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side.
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- A symmetric double convex lens with a focal length of 26.0 cmcm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surface? Express your answer to two significant figures and include the appropriate units.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…An optician is designing a contact lens. The material has is an index of refraction of 1.30. In order to yield the prescribed focal length, the optician specifies the following dimensions: inner radius of curvature = +2.46 cm outer radius of curvature = +2.02 cm where the inner radius of curvature describes the surface that touches the eye, and the outer radius of curvature describes the surface that first interacts with incoming light. What is the focal length of this contact lens (in cm)?