The distance between a 10 cm tall candle and the reflecting surface of a concave mirror is 40 cm. The radius of curvature of the mirror is 25 cm. Now,

A. What is the focal length of the mirror?
B. What is the image distance?
C. What is the magnification of the image?
D. What is the height of the image?
E. State whether the image is real or virtual and whether it is upright or inverted.

I'm honestly so confused

A. Focal length = half of radius of curvature = > f = 25/2=12.5 cm

B. 1/o+1/i=1/f, where o is the object distance, I is the image distance , and f is the focal length,
1/I =1/f-1/o= 1/12.5- 1/40 = > I = 18.2 cm.
C. Magnification = 12.5/(40-12.5) = 0.45
D. Height of image is 10•0.45= 4.5 cm
E. Object is outside the focal lenth => real and invert

A. Focal length = half of radius of curvature = > f = 25/2=12.5 cm

B. 1/di + 1/do = 1/f
1/di + 1/-40 = 1/-12.5
di = 18.18m

C. M = -di/do = 18.18/-40 = -.45
Since the magnitude of image M is less than 1, the image is diminished.

D. M = hi/ho
hi = M*ho = -.45 * 10= -4.5

E. The negative sign of image distance indicates that the image is formed in front of the mirror and so is real. The negative sign of height of image indicates that the image is inverted.

No worries! Let's break it down step by step to make things clear.

A. To find the focal length of the mirror, we can use the mirror equation, which is given as:

1/f = 1/v - 1/u

where f is the focal length, v is the image distance, and u is the object distance.

In this case, the object distance (u) is 40 cm. The mirror equation will then become:

1/f = 1/v - 1/40

B. To find the image distance (v), we can rearrange the mirror equation to solve for v:

1/v = 1/f + 1/u

Now, substitute the given values into the equation and solve for v.

C. To find the magnification of the image (m), we use the formula:

m = -v/u

D. To find the height of the image (h'), we use the magnification formula:

h' = m * h

where h is the height of the object.

In this case, the height of the object is given as 10 cm.

E. To determine whether the image is real or virtual, and whether it is upright or inverted, we need to consider the sign conventions. A positive value for v indicates a real image, while a negative value indicates a virtual image. An upright image has a positive magnification (m > 0), while a negative magnification (m < 0) indicates an inverted image.

Now let's calculate each step one by one.

No problem! I'll break down each part of the question for you step by step:

A. To find the focal length of the mirror, you can use the mirror formula:

1/f = 1/v - 1/u

where f is the focal length, v is the image distance, and u is the object distance. In this case, the object distance u is the distance between the candle and the mirror, which is given as 40 cm. The image distance v is not given directly, so we need to calculate it.

B. To find the image distance, we can use the mirror formula again. Rearranging the formula:

1/v = 1/f + 1/u

Now, plug in the values: u = 40 cm and f is what we need to find.

C. To find the magnification of the image, we can use the magnification formula:

magnification (m) = height of the image (h') / height of the object (h)

D. The height of the image can be found using the magnification formula. Given the height of the candle (h = 10 cm), we can calculate the height of the image.

E. To determine if the image is real or virtual, and if it is upright or inverted, you can use the sign convention of spherical mirrors. If the image distance (v) is positive, the image is real. If the image height (h') is positive, the image is upright. If both v and h' are negative, the image is real and inverted.

Now, let's go through each step and calculate the values:

A. To find the focal length:
1/f = 1/v - 1/u
Substitute u = 40 cm (object distance)
Solve for v to get the image distance.

B. Using the image distance (v):
1/v = 1/f + 1/u
Substitute u = 40 cm (object distance) and solve for v.

C. To find the magnification:
magnification (m) = h' / h
Substitute h = 10 cm (height of candle) and solve for h'.

D. To find the height of the image:
Use the magnification formula:
h' = m * h
Substitute m (magnification) and h (height of the candle) to calculate h'.

E. Determine if the image is real or virtual and if it is upright or inverted:
Check the signs of v (image distance) and h' (height of the image).

I hope this step-by-step breakdown helps in solving the problem. Let me know if you need further assistance with the calculations.