Thin Lens and Image Formation

Transcription

1 Pre-Lab Quiz / PHYS 4 Thin Lens and Image Formation Name Lab Section. What do you investigate in this lab?. The ocal length o a bi-convex thin lens is 0 cm. To a real image with magniication o, what is the object distance p? What is the image distance q? Is the image upright or inverted? (Answer: p=5 cm, q=30 cm, inverted) 3. The ocal length o a bi-convex thin lens is 0 cm. The ocal length o a convex-concave thin lens is -0 cm. I placing them in parallel and in close contact, what is the compound ocal length? (Answer: 0 cm)

2 4. For a red light beam, the reractive index o a thin lens is.50. For a blue light beam, the reractive index is.55. For the red light beam, the ocal length o the thin lens is 0.0 cm. For the blue light beam, what is the corresponding ocal length? (Answer: 9.4 cm)

3 Instructor s Lab Manual / PHYS 4 Thin Lens and Image Formation Name Lab Section Objective In this lab, you will measure the ocal length o thin lens, use thin lens to orm image and study the thin-lens equation, and observe the chromatic aberration o thin lens. Background Thin-lens equation Optics employs a variety o lenses or image ormation and spectroscopic measurement. In this lab, you will study how images are ormed through diraction by thin lenses. You will use two dierent kinds o thin lenses (Figure ): two bi-convex lenses (converging) and a convex-concave lens (diverging). A lens is characterized by its ocal points (F, F ) and ocal length (). For a converging lens, i the incident rays are parallel with its principle axis, the reracted rays by the lens converges at the ocal point on the same side o the lens as the reracted rays. For a diverging lens, i the incident rays are parallel with its principle axis, the reracted rays, when traced backward, converge at the ocal point on the same side o the lens as the incident rays. The ocal length,, is thus positive or a converging lens and is negative or a diverging lens; the magnitude o is the distance between the ocal point and the center o the lens. 3

4 As shown in Figure, i an object is placed near the principle axis o a thin lens, the ormed image through diraction by the thin lens is described by the thin-lens equation: + =. () p q The object distance, p, is the distance between the object and the center o the lens. The image distance, q, is the distance between the image and the center o the lens; q is positive or a real image and negative or a virtual image. The magniication o the image is: M image height q = () object height p The image height is positive or an upright image and negative or an inverted image. Place two thin lenses (respectively with the ocal length o and ) together such that their principle axes coincide (so they are parallel) and they are in contact. This combination o thin lenses behaves also like a thin lens. Using Equation (), it is straightorward to derive the compound ocal length as 4

5 = +. (3) Converging lens Because a converging lens has positive ocal length, ollowing Equation () a converging lens can orm both real and virtual images. I the object distance p<, Equation () leads to a negative q inerring a virtual image. I the object distance p>, Equation () leads to a positive q inerring a real image. Real images can directly project on a screen, enabling direct measurement o q and M. Thus, selecting an appropriate p, one can orm a real image, measure q, and use Equation () to calculate. Method Placing an object ar away rom the lens, p is much longer than. Equation () leads to q. Thus, a real image orms approximately at the ocal point F. Placing an object near F with p> but p, Equation () leads to a very large q. Thus, a very large real image orms on a screen placed ar away. These are simple methods to approximately measure the ocal length. Method Placing the object at p=3, Equation () leads to that q=.5. Method 3 Placing the object at p=, Equation () leads to that q=. Method 4 Placing the object p=.5, Equation () leads to that q=3. Diverging lens Because the ocal length o a diverging lens is negative, ollowing Equation (), it can orm only virtual images which cannot directly project on screen. According to Equation (3), i combing a diverging lens with a converging lens with a shorter ocal length, the compound ocal length is however positive and can thus be 5

6 measured directly. The ocal length o the diverging lens can then be extracted. Chromatic aberration The ocal length o a bi-convex thin lens placed in air ollows the lens-maker s equation = ( n )( + ). (4) R R where n is the reractive index o the lens. R is the radius o the curvature o its ront surace and R is the radius o the curvature o its back surace. Because the reractive index is dierent at dierent wavelengths, the ocal length varies with the wavelength. For example, n is smaller or red light than or blue light. Thus, the ocal length is longer or red light than or blue light, leading to the chromatic aberration or the lens. EXPERIMENT In this lab, the object, lens holder, and screen are placed on track and can move along the track. p and q are determined by reading their positions rom the attached rule on the track. Procedures. Measure the object size Use the calibrator to measure the object height. Recommend to measure the height o the arrow, h. Record it in Table.. Measure the ocal length o the irst bi-convex lens 6

7 (Method ) Place the lens on the lens holder. Move the screen to the opposite end o the track. Move the lens holder until you can see the sharpest image on the screen. Using the rule, determine the image distance between the lens holder and the screen which is approximately the ocal length,. Record it in Table. Move the lens holder towards the object; when their distance is about, you should see a very large and sharp image on the screen. (Method ) Move the lens holder away rom the object to make p 3. Then, move the screen until you can see the sharpest image on the screen. Using the rule, determine the image distance q between the lens holder and the screen. Record it in Table. Use the calibrator to measure the height o the arrow on the screen, h. Be careul with the sign o h. (Method 3) Move the lens holder towards the object to make p. Then, move the screen until you can see the sharpest image on the screen. Using the rule, determine the image distance q between the lens holder and the screen. Record it in Table. Use the calibrator to measure the height o the arrow on the screen. (Method 4) Move the lens holder towards the object to make p.5. Then, move the screen until you can see the sharpest image on the screen. Using the rule, determine the image distance q between the lens holder and the screen. Record it in Table. Use the calibrator to measure the height o the arrow on the screen. calculate Using Equation () and the p and q data rom Methods -4, TABLE - Lens p (cm) q M= q/p object image M=h /h 7

8 (~ Using Equation () and the p and q data rom Methods -4, calculate the corresponding ocal length and record in Table. Calculate their mean value and record it here: = Using the p and q data rom Methods -4, calculate M= -q/p and record in Table. Using the h and h data rom Methods -4, calculate M= h / h and record in Table. 3. Measure the chromatic aberration o the irst bi-convex lens Move the lens holder towards the object to make p.5. Now, place the red ilter on the object, and move the screen until you can see the sharpest image on the screen. Using the rule, determine the image distance q between the lens holder and the screen. Record it in Table. Now, place the blue ilter on the object, and move the screen until you can see the sharpest image on the screen. Using the rule, determine the image distance q between the lens holder and the screen. Record it in Table. Using Equation () and the p and q data, calculate the corresponding ocal length and record in Table. TABLE Chromatic Aberration 8

9 Red ilter Blue ilter p (cm) q (cm) (cm) 4. Measure the ocal length o the Plano-convex lens (converging) Place the lens on the lens holder. Move the object and the screen to the opposite ends o the rule. Move the lens holder until you can see the sharpest image on the screen. Using the rule, determine the image distance between the lens holder and the screen which is approximately the ocal length,. (Method 3) Move the lens holder towards the object to make p. Then, move the screen until you can see the sharpest image on the screen. Using the rule, determine the image distance q between the lens holder and the screen. = Record p = q= Using Equation () and the p and q data calculate the ocal length 5. Measure the compound ocal length or the two converging lenses Careully place the bi-convex lens and the plano-convex lens (in contact and in parallel) on the lens holder. Move the lens holder towards the object to make p +. Then, move the screen until seeing the sharpest image. Determine the image distance q between the lens holder and the screen. Record p = q= Using Equation () and the p and q data, calculate the compound ocal length & = 9

10 6. Measure the compound ocal length o the bi-convex lens & the plano-concave (diverging) lens Place the bi-convex lens and the plano-concave (in contact and in parallel) on the lens holder. Move the lens holder towards the object until p 3. Then, move the screen until seeing the sharpest image. Determine the image distance q between the lens holder and the screen. Record p = q= Using Equation (), calculate the compound ocal length: &3 = Using Equation (3),, and &3, calculate the ocal length o the diverging lens: 3 = Questions. In procedure, are all the images upright or inverted? What is the direction o the horizontal arrow on the screen?. Using the irst bi-convex lens to orm a magniied real image, in what range should the object distance be? 0

11 3. Using Equation (4) and the data in Table, calculate the ratio o the reractive index o the lens between the red light and the blue light. 4. Calculate + and compare it with the measured &. Calculate their dierence in percentage. Will & change i you switch the position o the two lenses in the combination? 5. For the combination o the diverging lens and the converging lens, what is the compound ocal length? Can you use this combination to measure the ocal length o the diverging lens?