Question

An object is located in water 15 cm from the vertex of a concave surface made of glass with a radius of curvature 10 cm. Where does the image by refraction form and what is its magnification? Use nwater=4/3 and nglass=1.5.

Answer 1

To find the image location and magnification caused by a concave glass surface, we apply the lensmaker's formula for refraction at a spherical surface. Using this equation along with the given refractive indices and object distance, we can solve for the image distance and magnification.

Step-by-step explanation:

To solve for the location and magnification of the image formed by a concave surface in water, we use the lensmaker's formula for refraction at a spherical surface, which is:

`\( (n_2)/(v) - (n_1)/(u) = (n_2 - n_1)/(R) \)`

Where:

• 
  `\( n_1 = 4/3 \)`(refractive index of water)
• 
  `\( n_2 = 1.5 \)` (refractive index of glass)
• 
  `\( u = -15 \)`cm (object distance, negative because object is on the same side from where the light enters)
• R is the radius of curvature, which should be positive for concave surface, so
  `\( R = +10 \)` cm

Magnification (M) can be calculated using the following formula:

`\( M = -(n_1 v)/(n_2 u) \)`

Solving for v gives us the image distance, which we can then use to find the magnification.