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SOLUTION(A) Find the position of the imageBecause the mirror is convex, its focal length is negative. Substitute into the mirror equation.9 =320.0 cm-8.00 cmSolve f...

Question

SOLUTION(A) Find the position of the imageBecause the mirror is convex, its focal length is negative. Substitute into the mirror equation.9 =320.0 cm-8.00 cmSolve for-5.71 cm(B) Find the magnification of the mirrorSubstitute into the magnification equation.M = -15.71 cm 20.0 cm0.286(C) Find the height of the image_Multiply the object height by the magnification.h' = hM = (3.00 cm)(0.286) 0.858 cm

SOLUTION (A) Find the position of the image Because the mirror is convex, its focal length is negative. Substitute into the mirror equation. 9 =3 20.0 cm -8.00 cm Solve for -5.71 cm (B) Find the magnification of the mirror Substitute into the magnification equation. M = -1 5.71 cm 20.0 cm 0.286 (C) Find the height of the image_ Multiply the object height by the magnification. h' = hM = (3.00 cm)(0.286) 0.858 cm



Answers

An object of height 2.00 $\mathrm{cm}$ is placed 30.0 $\mathrm{cm}$ from a convex spherical mirror of focal length of magnitude $10.0 \mathrm{cm} .$ (a) Find the location of the image. (b) Indicate whether
the image is upright or inverted. (c) Determine the height of the image.

In this question. We have a convex mirror. Peter googling is um negative 10 cm and then an object are displaced. The TCM away from the mirror. Okay. Has the height of the museum? Okay. So we want to find a location of the image and describe the image properties. So to do a Yeah he will be using the mirror equation. Yeah. Okay. One of the P has won over Q. He goes to one of the F. So uh one of a. Q. Is it good to one over negative 10 1/30. So we get negative for over 30. So Q. is negative. 7.5 cm. Okay, so the location of the image? Yeah. Okay. 7.5 cm behind the mirror because the queue is negative. Okay so the image will be behind the mirror. He said this is the answer for a and then for the image properties. Mhm. Okay. So we can say that this is uh true because Q is negative. So it's virtual. And then the magnification of the image mm is legal to negative Q. P. So we have 7.5 by 30 and the magnification is 0.25. Uh Image height is um and time stuff. Image of the object height. So um Okay so we have 0.25 times two And we got 0.5. Yeah. Okay. So the image is also right, Okay, because the image height is positive. All right, so the image properties virtual upright. Okay the magnification is 0.25. Image high is uh 0.5cm. King. and that's all for this question.

Yeah. Hello. We have a principle like this with kind of like some hero, let's say it's forgot pointers. Yeah. So the radius of curvature is twice on the fuck out. Right For calling the 15. Mhm. Do you take this blissed at a distance thin let's extend out for college. So enjoying this with a graph. You must make sure there is proportionality between F. M. R. So if you choose a distance of 10 cm. Asher F Irish 20 cm measures from the cool. So we replace our object you at the distance which is less than which is 10cm. So we measure things and to test give me a place. Yeah. Okay there. Yeah. Mhm. The first way that goes prime now. Mhm. The mirror is reflected says that there appears to have been coming from. Mhm. The focal point. And there was a really that an imaginary way that passes truth the radius of curvature and deviated. So at the intersecting point of these two ways we have a virtual image be informed. So the image is diminished. It is up right? Oh and it is virtually because it is formed by the intersection of operate race. Not really racing. Using the formula we can mm find. Yeah. I think I used all of our vehicles and this was the original form. I have uh one of our plus one of our first on the F. So I don't know it close -1/15. All over again, focal length is negative because it is a conquered a convex mirror. So if they cause negative for convex mirror. Mhm. Yeah. Mhm. So from this of the is negative six activities and magnification is by you Which is my Nigeria six. So again it is diminished. It is very strong because its image the status negative and uh yeah. So we can tell this to From the last four. Thank you for watching. Yeah.

In the first part of this problem, we're going to get the object and m in distance when the object lies beyond the center off. Correct. So we need to get that deal, which is the object Distance and de I, which is at a distance Well, the middle equipment as a wonder wanted by f X equals two one divided by deal plus one you wanted by the high where this effort, the vocal and off the mirror we got it equating about one. It is doing that This deal minus D I is equals to 45.0 center. So from here we can white This idea eyes equals true uh deal oneness 45.0 sentiment and we call it equating about two now and setting this weathering to equate number one along with the value off the focal. And we can write a query. Number one is when you wanted by 30 point is your sentiment is equals to one divided by Dior plus one day wanted by do your Wyness 45.0 centimeters So this can be written as it wonder wanted by 30.0 centimeter equals two here will be to Dior minus 45 point zero centimeter. You wanted by deal into a deal minus 45 points it listen to me. So this will give us and a question which is do a square minus 105 deal plus 108. 1350 and it is equal to zero. Now we can school is quiet and using the using the quadratic formula as a do equals two minus into 100 minus 105 plus minus. Squared off minus 105. Old square minus. Fall into one into 1350 on the square root is up to this point you wanted by two into one. So there you are, sir. The very 40 as equals two 1 to 5 plus minus 75.0. So what is 75.0? Do wanted by to we call it equating about three. So from here we can get to values two questions one with plus sign and one with minus No for the case where object lies beyond the center of nature. We can wipe this quiet and as the deal is equals to 105 centimeter blood. So 1 to 5.0 centimeter rewarded by to So this was your The value for the deal, as do is equals to 90.0 centimeters. So no, you leave with number to become white demand for the for the D I as a the eyes equals two, uh, 90.0 centimeter minus 45 point zero sentiment. So we will get the battle for the i. D. I Z equals two 45 points in the sentiment. Now when the object lies between the focal and 10 the mirror the question will be do your prime and it is equals to 105 centimeter minus So 25 centimeter divided by two. So this would you rather for you said your prime as a your brand is equals to 15 points Little sentiment similarly, we can get the value for D. I prime is Do you have prime is it goes to, uh 15 points little centimeter minus 45.7 centimeters. So we get the value for the Saudi. I primary their prime musicals too minus 30 point zero centimeters. So end of the cushion. Thank you

Hi. In the given problem there is a donkey spherical mirror bulls for talent is given as F is equal to plus 30.0 centimetre and the distance between the positions of the image and the object in front of this concave is very cool mirror. Or given us if this is the center of curvature, this will be the focal land. If the object is here we know the image forms will be here. So if this is the object that stands from the vertex of this mirror, D. O. Then here it will become the image distance D. I. So the gap between object and the image formed which may be either it may be D or minus D. I. If the object is beyond the center of curvature then object distance will be more. The image will be formed between the optical center and the principal focus. In that case this is D. O minus D. I. Is equal to 45 10 centimeter. And and in the second case, if the object is lying between central asia and the focus, principal focus, then the image will be formed beyond central characters. So now it will become geo uh sorry D. I minus deal And that is same 45.0 centimetre. And as you know the positions of the object and image in front of the concave mirror are interchangeable. So we will find only one of the answer this given problem. Then another answer will be in ter convertible. So in the first part of the problem yeah the object lies beyond center of curvature. Then definitely image will be lying between central curvature and principal focus. So this will be to your minus D. is equal to 45 cm. So using that we get an expression for D. I. In terms of deal. So this D. I will be Video object stands -45. So using mirror equation, which is a relation among the object distance deal the industry sends li I earned our focal length. So here it will be for video. This will be the same as D. O. Or D. I. This is one by D. All -45 Is equal to focal length, which is 31 x 30 centimetre. Now taking an L. C. M. Here this is do you Braggadocio -45. And here it will be deal -45 plus. The old Is equal to one x 30. Or we can say this is advise of deal -45 divided by D. O. Square, expanding the bracket. Opening this bracket, do you square minus 45 G. O. Which is equal to one x 30. When making a cross multiplication. We get here if you multiply this 30 but this and this. So it will become 60 G. O -1350 is equal to D. O. Square minus 45. The oh so finally rearranging all these terms we get a quadratic equation. Do you square -105 d. O plus 1000 350 is equal to zero? Which is a quadratic equation of the form a X square plus bx plus C is equal to zero. And the solution of such a quadratic equation is given with the help of the screaming and and here the discriminate is B squared minus for a C. So the root of the situation will be deal Is equal to -7. These -105. Let's minus D. Discriminate. Which is actually b squared minus four is easy for me. This is 0 5 -4. A for Amy's the multiple of Geo Square which is one. C means 1350 Divided by two aims to into one again. Saw Yeah it will come out to be This is 105. Bless minus For the square of this. 105. You will come out to be 11025 and then it will come out to be minus 5000 or hunted. Do you fight it by two? Then this is 100 and five plus minus the square root off It will come out to be 5000 625 Divided by two. So this is D. Oh Is equal to 105. Last 75 divided by two. Again. Now taking the positive sign there are two possibilities. So first of all, if we take positive sign, This deal means the object distance will be 105 plus 75, which is 180 divided by two. Yes, this is 90 cm. And if we take negative sign here, This video will be 105 -75. So it will be 30 x two means 15 centimeter. But this Value of D. O. Which is equal to 15 cm, will not be possible because the distance between D. U. And D. I. Is only 45 is 45 centimeter. So the value of D. O less than 45 centimeter is not possible. So the only possible answer for D. O. Is 90.0 centimetre. So D. I means the distance of image there will be because we have used for it As their equals to deal -45. So this D. I 90 minus 45 means this is 45 centimeter. So these are the two answers for the First part of the problem object has been kept at a distance of 90 cm and images being formed at a distance of 45cm in front of the concave mirror. No, in the second part of the problem, as we know as the distances of the positions of object and image its image four, a spherical mirror are interchangeable. Therefore, in the 2nd case, and object will be lying at a distance less than the radius of curvature means which will be lying before the center of gravity. Sure. Then the image will be lying beyond the center of curvature. Means in this case Now video will become 45 cm, So DI will now become 90 centimetre. So these two are the answers for the second part of the same problem. Thank you.


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