Using the thin lens and free space ray transfer matrices, find the image plane X. An object is placed at 3f from the lens of focal length f. Recall that the imaging condition holds that rays should converge in the image plane as a function of their height in the object plane (y1₁), and should not depend on their initial angle (0₁).
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Q: Homework 11, Problem 3
A: Step 1: Step 2: Step 3: don't forget to upvote thank you :) comment if doubt exists Step 4:
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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 lensb. 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?A light propagates in Material 1 with index of refraction n1 = 1.13, strikes an interface, then passes into Material 2 with an index of refraction n2 = 1.41. The angle of incidence at the interface is 27.5. Determine the angle of refractionFigure 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…
- One positive lens (focal length = f1) and one negative lens (focal length = -f2) are placed at a distance d. – All lenses are thin lenses. Find the overall ABCD matrix of the system Find the value of d when “C” of the overall matrix is zero. ( Hint : Find d in terms of f1 and f2) (This is when the focal length of the overall system is infinity.)In the figure, a real inverted image I of an object O is formed by a certain lens (not shown); the object-image separation is d, measured along the central axis of the lens. The image is just 1/4 the size of the object. (a) How far from the object must the lens be placed? NOTE: Express your answers in terms of the given variables. Р (b) What is the focal length of the lens? f = O Lens here d Axis 1↓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 cm
- Homework 11, Problem 3A scene point with coordinate (X, Y, Z) = (α, β, γ) in the world is perspectively projected into an image at coordinate (x, y) = (δ, ϵ), where both coordinates are given in millimeters in the camera coordinate frame and the camera’s principal point is at coordinates (0, 0, f). The camera reference frame is translated ζ mm in the negative direction along the z-axis relative to the world reference frame. What are values for the camera intrinsics and extrinsics? Show all your work.Let IB and OB be distances from the plane mirror to the image and object, respectively. Show that IB = OB. Prove that image and object have the same size.
- Consider the lens–mirror arrangement as shown. There are two final image positions to the left of the lens of focal length fL. One image position is due to light traveling from the object to the left and passing through the lens. The other image position is due to light traveling to the right from the object, reflecting from the mirror of focal length fM and then passing through the lens. For a given object position p between the lens and the mirror and measured with respect to the lens, there are two separation distances d between the lens and mirror that will cause the two images described above to be at the same location. Find both positions.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.A horizontal light ray is incident on a crown glass prism as shown in the figure where β = 27.8°. Find the angle of deviation δ of the ray—the angle that the ray emerging from the prism makes with the incident ray.