A hand- made projector employs a concave mirror to project an image onto a screen. If an object with a height of 4 cm is positioned 15 cm in front of the concave mirror with focal length 10 cm, at what distance should the screen be located to capture a sharp image and also calculate the height of the image formed on the screen.30 cm and 8 cm respectively30 cm and 6 cm respectively15 cm and 8 cm respectively15 cm and 6 cm respectively
Question
A hand- made projector employs a concave mirror to project an image onto a screen. If an object with a height of 4 cm is positioned 15 cm in front of the concave mirror with focal length 10 cm, at what distance should the screen be located to capture a sharp image and also calculate the height of the image formed on the screen.30 cm and 8 cm respectively30 cm and 6 cm respectively15 cm and 8 cm respectively15 cm and 6 cm respectively
Solution
To solve this problem, we can use the mirror formula and magnification formula.
The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Given that f = 10 cm and u = -15 cm (the negative sign indicates that the object is on the same side of the mirror as the light source), we can substitute these values into the mirror formula to find v:
1/v = 1/f - 1/u 1/v = 1/10 - 1/(-15) 1/v = 1/10 + 1/15 1/v = (3 + 2) / 30 1/v = 5/30 v = 30/5 v = 6 cm
The negative sign indicates that the image is formed on the same side as the light source. Therefore, the screen should be located 6 cm from the mirror.
The magnification formula is m = -v/u = h'/h, where m is the magnification, h' is the height of the image, and h is the height of the object.
Substituting the given and calculated values into the magnification formula, we find:
m = -v/u = h'/h -6/-15 = h'/4 h' = 4 * 6/15 h' = 1.6 cm
Therefore, the height of the image formed on the screen is 1.6 cm.
So, none of the given options are correct. The screen should be located 6 cm from the mirror, and the height of the image formed on the screen is 1.6 cm.
Similar Questions
An object 5 cm high is placed at a distance 60 cm in front of a concave mirror of focal length 10 cm. Find the position and size of the image by drawing.
An object of height 4.5 cm is placed 32 cm in front of a concave mirror with a radius ofcurvature of 19 cm.(i) Draw a ray diagram to show the location of the image formed by the mirror andstate whether the image is real or virtual. [3 marks](ii) Calculate the distance of the image from the mirror. [3 marks](iii) Calculate the magnification of the image
A 6 cm tall object is placed at a distance 18 cm from a concave mirror. If the image formed is half the size of the object and is inverted, determine the focal length of the mirror.9 cm18 cm-6 cm-12 cm
A makeup artist uses a concave mirror with a focal length of 12 cm to apply makeup with precision. If the client's face is positioned 24 cm from the mirror, how far is the image of the face located from the mirror's surface?-8 cm-24 cm+8 cm+24 cm
When an object of height 1 cm is kept at a distance 4 cm from a concave mirror, its erect image of height 1.5 cm is formed at a distance 6 cm behind the mirror. Find the focal length of mirror, by draw
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.