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A person suffers from hypermetropia (long sight) - AQA - A-Level Physics - Question 1 - 2017 - Paper 5
Question 1
A person suffers from hypermetropia (long sight). Use of a spectacle lens of power +2.0D allows the person to just see clearly an object placed 24 cm away from the e... show full transcript
Worked Solution & Example Answer:A person suffers from hypermetropia (long sight) - AQA - A-Level Physics - Question 1 - 2017 - Paper 5
Step 1
Explain why the unaided defective eye cannot form a clearly focused image of the object placed 24 cm from the eye.
Answer
The unaided eye of a person with hypermetropia cannot focus on nearby objects because the eye lens is unable to bend light rays sufficiently. Specifically, they may be too weak or the eyeball may be too short, preventing the light rays from converging on the retina. As a result, the image is either unfocused or appears blurry.
Step 2
Calculate the distance of the image formed from the spectacle lens.
Answer
To calculate the image distance ( v ), we can use the lens formula:
\frac{1}{f} = \frac{1}{u} + \frac{1}{v}
where:
- f = focal length of the lens = \frac{1}{power} = \frac{1}{+2.0} = 0.5 m = 50 cm
- u = object distance = -24 cm (negative as per lens convention)
Substituting values:
Rearranging gives:
Calculating this, we find: v ≈ 16.56 cm
Therefore, the image distance is approximately 16.6 cm, when rounded to two significant figures.
Step 3
Step 4
Draw a ray diagram to show how this spectacle lens forms an image of the object placed 24 cm from the spectacle lens.
Answer
For the ray diagram:
- Start by drawing a line for the spectacle lens.
- Draw an object arrow at 24 cm from the lens.
- Depict two rays from the top of the object:
- One ray parallel to the principal axis, refracting through the lens and passing through the focal point.
- A second ray passing through the center of the lens, which continues in a straight line.
- Mark the location where the two rays converge, indicating the image's position.
- Label the object, image, and the principal focus of the lens.