Consider an object and a screen at a fixed distance d = 50 cm from each other.  For the convex lens of focal distance f = 10 cm, demonstrate mathematically that there are two solutions if and only if do + di = d is larger than 4 times the focal distance f of the lens. Make a diagram.

Work with your neighbors to fill in the table below. If a number has (+) written in front of it, then you must determine if the number should be positive or negative. mirror type concave focal radius of length curv. (+)20 cm +20 cm -40 cm object image magnifi- distance distance cation +10 cm +10 cm +30 cm -10 cm 1.0 real or virtual? inverted. or not?

Spherical refracting surfaces. When an object is placed 9.3 cm in front of a spherical refracting surface the image distance is -15 cm. The index of refraction of the refracting material is 2.7 and it is embedded in transparent material with index of refraction 2.0. Find (a) the radius of curvature r of the surface (including the sign) and determine whether the image is (b) real or virtual and (c) on the same side of the surface as object O or on the opposite side. (a) (b) (c) n1 n2 pr i R/V Side 2.0 2.7 +9.3 -15 (a) Number Units (b) (c) >

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Problem 1: Two convex lenses which share a common principal axis are separated by a distance which is greater than the sum of their focal lengths, as shown. -L- F1 F1 F2 F2 lens 1 lens 2 Lens 1, with focal length F1, is placed to the left. Lens 2, with focal length F2, is placed a distance L to the right of the first lens. Part (a) An object is placed a distance do1 =26.5 cm to the left of lens 1 which has focal length F =4.8 cm. Ignore the existence of lens 2 for the moment. What is the position of the image, d;,1 created by lens 1? Include the sign which is consistent with standard sign conventions. Numeric : A numeric value is expected and not an expression. di,1 Part (b) Calculate the magnification, M1, of lens 1 for the object as positioned in the previous step. Be certain to include the sign that is consistent with the standard conventions. Numeric : A numeric value is expected and not an expression. M1 = Part (c) Which statement best describes the image created by lens 1?…

An object is placed to the left of two converging lenses, as shown in (Figure 1). Lens 1 has a focal length f and lens 2 has a focal length 2f. The lenses are separated by a distance of 6 f. An object of height h is then placed a distance of 2f to the left of lens 1. Calculate the following quantities in terms of f and h (specify the Figure "↑ 1 of 1 Part A Start solving the problem by constructing a sketch of the lens system and indicating the focal points of each lens. Write down the thin-lens equation. Express your answer in terms of the focal length f, the object so, and image si distances, if needed. ► View Available Hint(s) VE ΑΣΦ 16f 3 Submit Previous Answers ? X Incorrect; Try Again; 5 attempts remaining

In the following three scenarios, an object is located on one side of a converging lens. In each case, you must determine if the lens forms an image of this object. If it does, you also must determine the following. whether the image is real or virtual whether the image is upright or inverted the image's location, q the image's magnification, M The focal length is  f = 60.0 cm  for this lens. Set both q and M to zero if no image exists. Note: If q appears to be infinite, the image does not exist (but nevertheless set q to 0 when entering your answers to that particular scenario). (a) The object lies at position 60.0 cm. (Enter the value for q in cm.) q= cmM= Select all that apply to part (a).  realvirtualuprightinvertedno image (b) The object lies at position 7.06 cm. (Enter the value for q in cm.) q= cmM= Select all that apply to part (b).  realvirtualuprightinvertedno image (c) The object lies at position 300 cm. (Enter the value for q in cm.) q= cmM= Select all that…

Part A: State the characteristics of the image formed by a converging lens when the object is distance is less than the focal length of the lens. An object (2.0 mm high) is place at a distance of 30 cm in front of a diverging lens of focal length 20 cm.  Calculate the image distance of the image produced by the lens and verify all the characteristics listed in question (2).

More lenses. Object O stands on the central axis of a thin symmetric lens. For this situation (see the table below, all distances are in centimeters), find (a) the lens type, converging or diverging. (b) the focal distance f, (c) the image distance i. It also refers to whether (d) the image is real or virtual, (e) inverted or noninverted from 0, and (f) on the same side of the lens as O or on the opposite side. (a) (b) (c) (d) (e) (f) Туре f p i m R/V I/NI Side +26 +1.27 (a) (b) Number i Units (c) Number i Units (d) (e) (f)

Two thin lenses with focal lengths of magnitude 15.0 cm, the first diverging and the second converging, are placed 12.00 cm apart. An object 3.00 mm tall is placed 5.50 cm to the left of the first (diverging) lens. Where is the image formed by the first lens located? Please provide a detailed explanation of the process. How far from the object is the final image formed? Please describe the steps taken to reach to your conclusion.